> #restart; read `d:/Ake/tf/ToadsAndFrogs.txt`; > Prove(3,2,a,A32); ##Conjectures## ############################# Let, f[1], be the value of , [T $ a[1], B, T $ a[2], B, T $ a[3], B, T $ a[4], F, T $ a[5], F] ############################# f[1](0, 0, 0, 0, 0) = [-6] f[1](1, 0, 0, 0, 0) = [{[-2]}, {[-2]}] f[1](a[1], 0, 0, 0, 0) = [{[a[1] - 2]}, {[a[1] - 2]}], 2 <= a[1] f[1](0, 1, 0, 0, 0) = [-2] f[1](a[1], 1, 0, 0, 0) = [a[1] - 1], 1 <= a[1] f[1](a[1], 2, 0, 0, 0) = [{[2 a[1] - 1]}, {[a[1]]}], 0 <= a[1] f[1](a[1], a[2], 0, 0, 0) = [{[2 a[1] + a[2] - 5/2]}, {[a[1]]}], 3 <= a[2], 0 <= a[1] f[1](0, 0, 1, 0, 0) = [-3] f[1](a[1], 0, 1, 0, 0) = [{[2 a[1] - 3]}, {[a[1] - 1]}], 1 <= a[1] f[1](a[1], 1, 1, 0, 0) = [2 a[1] - 1], 0 <= a[1] f[1](a[1], a[2], 1, 0, 0) = [2 a[1] + a[2] - 3/2], 2 <= a[2], 0 <= a[1] f[1](0, 0, 2, 0, 0) = [{[-1]}, {[-1]}] f[1](1, 0, 2, 0, 0) = [{[1]}, {[1]}] f[1](a[1], 0, 2, 0, 0) = [2 a[1] - 3/2], 2 <= a[1] f[1](0, 1, 2, 0, 0) = [{[1/2]}, {[1/2]}] f[1](a[1], 1, 2, 0, 0) = [2 a[1]], 1 <= a[1] f[1](a[1], a[2], 2, 0, 0) = [2 a[1] + a[2] - 1], 2 <= a[2], 0 <= a[1] f[1](a[1], a[2], a[3], 0, 0) = [{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}], 0 <= a[2], 3 <= a[3], 0 <= a[1] f[1](0, 0, 0, 1, 0) = [-4] f[1](1, 0, 0, 1, 0) = [-1] f[1](a[1], 0, 0, 1, 0) = [a[1] - 1], 2 <= a[1] f[1](0, 1, 0, 1, 0) = [{[-1]}, {[-1]}] f[1](1, 1, 0, 1, 0) = [{[1]}, {[1]}] f[1](a[1], 1, 0, 1, 0) = [ {[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}], 2 <= a[1] f[1](0, 2, 0, 1, 0) = [{[1/2]}, {[1/2]}] f[1](a[1], 2, 0, 1, 0) = [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], 1 <= a[1] f[1](a[1], a[2], 0, 1, 0) = [ {[{[2 a[1] + a[2] - 2]}, {[2 a[1] + a[2] - 2]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], 3 <= a[2], 0 <= a[1] f[1](0, 0, 1, 1, 0) = [{[0]}, {[{[-1]}, {[-1]}]}] f[1](1, 0, 1, 1, 0) = [{[3]}, {[{[1]}, {[1]}]}] f[1](a[1], 0, 1, 1, 0) = [{[3 a[1]]}, {[ {[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}]}], 2 <= a[1] f[1](0, 1, 1, 1, 0) = [{[2]}, {[{[1/2]}, {[1/2]}]}] f[1](a[1], 1, 1, 1, 0) = [{[3 a[1] + 2]}, { [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} ], 1 <= a[1] f[1](a[1], a[2], 1, 1, 0) = [{[3 a[1] + 2 a[2]]}, {[ {[{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}], 2 <= a[2], 0 <= a[1] f[1](a[1], a[2], a[3], 1, 0) = [{[3 a[1] + 2 a[2] + a[3] - 1]}, {[{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}]}], 0 <= a[2], 2 <= a[3], 0 <= a[1] f[1](a[1], a[2], a[3], a[4], 0) = [3 a[1] + 2 a[2] + a[3]], 0 <= a[2], 2 <= a[4], 0 <= a[1], 0 <= a[3] f[1](0, 0, 0, 0, 1) = [-5] f[1](1, 0, 0, 0, 1) = [{[-1]}, {[-1]}] f[1](2, 0, 0, 0, 1) = [{[1]}, {[1]}] f[1](a[1], 0, 0, 0, 1) = [ {[{[{[2 a[1] - 4]}, {[2 a[1] - 4]}]}, {[a[1] - 1/2]}]}, {[a[1] - 1]}], 3 <= a[1] f[1](0, 1, 0, 0, 1) = [-1] f[1](1, 1, 0, 0, 1) = [1] f[1](a[1], 1, 0, 0, 1) = [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}], 2 <= a[1] f[1](a[1], a[2], 0, 0, 1) = [{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}], 2 <= a[2], 0 <= a[1] f[1](0, 0, 1, 0, 1) = [-3/2] f[1](1, 0, 1, 0, 1) = [1/2] f[1](a[1], 0, 1, 0, 1) = [{[2 a[1] - 2]}, {[2 a[1] - 2]}], 2 <= a[1] f[1](a[1], 1, 1, 0, 1) = [2 a[1]], 0 <= a[1] f[1](a[1], a[2], 1, 0, 1) = [{[{[2 a[1] + a[2] - 1]}, {[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}]}, {[{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}], 2 <= a[2], 0 <= a[1] f[1](a[1], 0, 2, 0, 1) = [{[2 a[1]]}, {[2 a[1]]}], 0 <= a[1] f[1](a[1], a[2], 2, 0, 1) = [{[{[3 a[1] + 2 a[2]]}, {[{[2 a[1] + a[2]]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}]}, {[2 a[1] + a[2]]}], 0 <= a[1], 1 <= a[2] f[1](a[1], a[2], a[3], 0, 1) = [ {[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[2 a[1] + a[2] + 1/2]}]}, {[2 a[1] + a[2]]}], 0 <= a[2], 3 <= a[3], 0 <= a[1] f[1](a[1], 0, 0, 1, 1) = [2 a[1] - 2], 0 <= a[1] f[1](a[1], 1, 0, 1, 1) = [{[2 a[1]]}, {[2 a[1]]}], 0 <= a[1] f[1](a[1], a[2], 0, 1, 1) = [%1, {[ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}] , 2 <= a[2], 0 <= a[1] %1 := {[2 a[1] + a[2] - 1]} f[1](0, 0, 1, 1, 1) = [{[0]}, {[{[0]}, {[0]}]}] f[1](a[1], 0, 1, 1, 1) = [{[3 a[1]]}, {[{[2 a[1]]}, {[1 + a[1]]}]}] , 1 <= a[1] f[1](a[1], a[2], 1, 1, 1) = [{[3 a[1] + 2 a[2]]}, {[{[2 a[1] + a[2]]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}], 0 <= a[1], 1 <= a[2] f[1](a[1], a[2], a[3], 1, 1) = [{[3 a[1] + 2 a[2] + a[3] - 1]}, {[2 a[1] + a[2] + 1/2]}], 0 <= a[2], 2 <= a[3], 0 <= a[1] f[1](a[1], a[2], a[3], a[4], 1) = [3 a[1] + 2 a[2] + a[3]], 0 <= a[2], 2 <= a[4], 0 <= a[1], 0 <= a[3] f[1](0, 0, 0, 0, a[5]) = [-3], 2 <= a[5] f[1](a[1], 0, 0, 0, a[5]) = [{[2 a[1] - 2]}, {[2 a[1] - 2]}], 1 <= a[1], 2 <= a[5] f[1](a[1], a[2], 0, 0, a[5]) = [2 a[1] + a[2] - 1], 0 <= a[1], 1 <= a[2], 2 <= a[5] f[1](a[1], 0, 1, 0, a[5]) = [2 a[1] - 1], 0 <= a[1], 2 <= a[5] f[1](a[1], a[2], 1, 0, a[5]) = [{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}], 0 <= a[1], 1 <= a[2], 2 <= a[5] f[1](a[1], a[2], a[3], 0, a[5]) = [ {[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[1 + 2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}], 0 <= a[2], 2 <= a[3], 0 <= a[1], 2 <= a[5] f[1](0, 0, 0, 1, a[5]) = [-2], 2 <= a[5] f[1](a[1], 0, 0, 1, a[5]) = [{[2 a[1] - 1]}, {[2 a[1] - 1]}], 1 <= a[1], 2 <= a[5] f[1](a[1], a[2], 0, 1, a[5]) = [2 a[1] + a[2]], 0 <= a[1], 1 <= a[2], 2 <= a[5] f[1](a[1], a[2], a[3], 1, a[5]) = [{[3 a[1] + 2 a[2] + a[3] - 1]}, {[1 + 2 a[1] + a[2]]}], 0 <= a[2], 0 <= a[1], 2 <= a[5], 1 <= a[3] f[1](a[1], a[2], a[3], a[4], a[5]) = [3 a[1] + 2 a[2] + a[3]], 0 <= a[2], 2 <= a[4], 0 <= a[1], 0 <= a[3], 2 <= a[5] ############################# Let, f[2], be the value of , [T $ a[1], B, T $ a[2], B, T $ a[3], F, T $ a[4], B, T $ a[5], F] ############################# f[2](0, 0, 0, 0, 0) = [-5] f[2](0, 0, 0, 1, 0) = [-3] f[2](0, 0, 0, a[4], 0) = [{[{[a[4] - 4]}, {[-1]}]}, {[-2]}], 2 <= a[4] f[2](1, 0, 0, 0, 0) = [-2] f[2](a[1], 0, 0, 0, 0) = [a[1] - 2], 2 <= a[1] f[2](0, 1, 0, 0, 0) = [{[-2]}, {[-2]}] f[2](a[1], 1, 0, 0, 0) = [{[a[1] - 1]}, {[a[1] - 1]}], 1 <= a[1] f[2](0, 2, 0, 0, 0) = [{[-1/2]}, {[-1/2]}] f[2](a[1], a[2], 0, 0, 0) = [a[1]], 3 <= a[2], 0 <= a[1] f[2](a[1], 2, 0, 0, 0) = [a[1]], 1 <= a[1] f[2](0, 0, 1, 0, 0) = [-2] f[2](a[1], 0, 1, 0, 0) = [a[1] - 1], 1 <= a[1] f[2](a[1], 1, 1, 0, 0) = [{[2 a[1] - 1]}, {[a[1]]}], 0 <= a[1] f[2](a[1], a[2], 1, 0, 0) = [{[2 a[1] + a[2] - 3/2]}, {[a[1]]}], 2 <= a[2], 0 <= a[1] f[2](a[1], 0, 2, 0, 0) = [2 a[1] - 1], 0 <= a[1] f[2](a[1], a[2], 2, 0, 0) = [2 a[1] + a[2] - 1/2], 0 <= a[1], 1 <= a[2] f[2](a[1], 0, 3, 0, 0) = [{[{[2 a[1]]}, {[2 a[1]]}]}, {[2 a[1]]}], 0 <= a[1] f[2](a[1], a[2], 3, 0, 0) = [ {[{[{[3 a[1] + 2 a[2]]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, %1]} , %1], 0 <= a[1], 1 <= a[2] %1 := {[2 a[1] + a[2]]} f[2](a[1], a[2], a[3], 0, 0) = [{[ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[2 a[1] + a[2] + 1/2]}]}, {[2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}], 0 <= a[2], 0 <= a[1], 4 <= a[3] f[2](1, 0, 0, 1, 0) = [-1/2] f[2](a[1], 0, 0, 1, 0) = [{[a[1] - 1]}, {[a[1] - 1]}], 2 <= a[1] f[2](a[1], 0, 0, a[4], 0) = [{[{[2 a[1] + a[4] - 4]}, {[a[1]]}]}, {[a[1] - 1]}], 2 <= a[4], 1 <= a[1] f[2](0, 1, 0, 1, 0) = [-1] f[2](0, 1, 0, a[4], 0) = [{[{[{[-2 + a[4]]}, {[-2 + a[4]]}]}, {[1/2]}]}, {[-1/2]}], 2 <= a[4] f[2](a[1], 1, 0, 1, 0) = [a[1]], 1 <= a[1] f[2](a[1], 1, 0, a[4], 0) = [{[ {[{[2 a[1] + a[4] - 2]}, {[2 a[1] + a[4] - 2]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}, {[{[a[1]]}, {[a[1]]}]}], 2 <= a[4], 1 <= a[1] f[2](0, 2, 0, 1, 0) = [1/2] f[2](a[1], 2, 0, 1, 0) = [{[1 + a[1]]}, {[1 + a[1]]}], 1 <= a[1] f[2](a[1], a[2], 0, 1, 0) = [{[1 + a[1]]}, {[1 + a[1]]}], 3 <= a[2], 0 <= a[1] f[2](a[1], a[2], 0, 2, 0) = [{[ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}], 2 <= a[2], 0 <= a[1] %1 := {[2 a[1] + a[2] - 1]} f[2](a[1], a[2], 0, a[4], 0) = [{[{ [{[2 a[1] + a[2] + a[4] - 3]}, {[2 a[1] + a[2] + a[4] - 3]}]} , {[{[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}]} , {[{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}], 2 <= a[2], 0 <= a[1], 3 <= a[4] f[2](0, 0, 1, 1, 0) = [{[-1]}, {[-1]}] f[2](1, 0, 1, 1, 0) = [{[1]}, {[1]}] f[2](a[1], 0, 1, 1, 0) = [ {[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}], 2 <= a[1] f[2](0, 1, 1, 1, 0) = [{[1/2]}, {[1/2]}] f[2](a[1], 1, 1, 1, 0) = [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], 1 <= a[1] f[2](a[1], a[2], 1, 1, 0) = [ {[{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], 2 <= a[2], 0 <= a[1] f[2](0, 0, 1, a[4], 0) = [{[{[-2 + a[4]]}, {[0]}]}, {[-1]}], 2 <= a[4] f[2](a[1], 0, 1, a[4], 0) = [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}]}, {[a[1]]}], 2 <= a[4], 1 <= a[1] f[2](a[1], a[2], 1, a[4], 0) = [{[{[2 a[1] + a[2] + a[4] - 2]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}, {[a[1] + 2], [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}], 2 <= a[4], 0 <= a[1], 1 <= a[2] f[2](a[1], a[2], a[3], 1, 0) = [{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}], 0 <= a[2], 2 <= a[3], 0 <= a[1] f[2](a[1], a[2], a[3], a[4], 0) = [ {[{[2 a[1] + a[2] + a[4] - 2]}, {[1 + 2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}], 0 <= a[2], 2 <= a[4], 2 <= a[3], 0 <= a[1] f[2](0, 0, 0, 0, 1) = [-4] f[2](0, 0, 0, a[4], 1) = [{[a[4] - 3]}, {[-1]}], 1 <= a[4] f[2](1, 0, 0, 0, 1) = [-1] f[2](a[1], 0, 0, 0, 1) = [a[1] - 1], 2 <= a[1] f[2](0, 1, 0, 0, 1) = [{[-1]}, {[-1]}] f[2](1, 1, 0, 0, 1) = [{[1]}, {[1]}] f[2](a[1], 1, 0, 0, 1) = [ {[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}], 2 <= a[1] f[2](0, 2, 0, 0, 1) = [{[1/2]}, {[1/2]}] f[2](a[1], 2, 0, 0, 1) = [1 + a[1]], 1 <= a[1] f[2](a[1], a[2], 0, 0, 1) = [1 + a[1]], 3 <= a[2], 0 <= a[1] f[2](0, 0, 1, 0, 1) = [-1] f[2](1, 0, 1, 0, 1) = [1] f[2](a[1], 0, 1, 0, 1) = [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}], 2 <= a[1] f[2](a[1], a[2], 1, 0, 1) = [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}], 0 <= a[1], 1 <= a[2] f[2](a[1], a[2], a[3], 0, 1) = [2 a[1] + a[2]], 0 <= a[2], 2 <= a[3], 0 <= a[1] f[2](a[1], 0, 0, a[4], 1) = [{[2 a[1] + a[4] - 3]}, {[a[1]]}], 1 <= a[1], 1 <= a[4] f[2](0, 1, 0, a[4], 1) = [{[{[a[4] - 1]}, {[a[4] - 1]}]}, {[1/2]}], 1 <= a[4] f[2](a[1], 1, 0, a[4], 1) = [ {[{[2 a[1] - 1 + a[4]]}, {[2 a[1] - 1 + a[4]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], 1 <= a[1], 1 <= a[4] f[2](a[1], a[2], 0, 1, 1) = [ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}], 2 <= a[2], 0 <= a[1] %1 := {[2 a[1] + a[2] - 1]} f[2](a[1], a[2], 0, a[4], 1) = [{ [{[2 a[1] + a[2] + a[4] - 2]}, {[2 a[1] + a[2] + a[4] - 2]}]} , {[{[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}], 2 <= a[4], 2 <= a[2], 0 <= a[1] f[2](0, 0, 1, a[4], 1) = [{[a[4] - 1]}, {[0]}], 1 <= a[4] f[2](a[1], 0, 1, a[4], 1) = [{[2 a[1] - 1 + a[4]]}, {[1 + a[1]]}], 1 <= a[1], 1 <= a[4] f[2](a[1], a[2], 1, a[4], 1) = [{[a[4] + 2 a[1] + a[2] - 1]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}], 0 <= a[1], 1 <= a[2], 1 <= a[4] f[2](a[1], a[2], a[3], a[4], 1) = [{[a[4] + 2 a[1] + a[2] - 1]}, {[1 + 2 a[1] + a[2]]}], 0 <= a[2], 2 <= a[3], 0 <= a[1], 1 <= a[4] f[2](a[1], 0, 0, a[4], a[5]) = [2 a[1] + a[4] - 2], 0 <= a[1], 2 <= a[5], 0 <= a[4] f[2](a[1], a[2], 0, a[4], a[5]) = [{[a[4] + 2 a[1] + a[2] - 1]}, {[a[4] + 2 a[1] + a[2] - 1]}], 0 <= a[1], 1 <= a[2], 2 <= a[5], 0 <= a[4] f[2](a[1], a[2], a[3], a[4], a[5]) = [a[4] + 2 a[1] + a[2]], 0 <= a[2], 0 <= a[1], 2 <= a[5], 1 <= a[3], 0 <= a[4] ############################# Let, f[3], be the value of , [T $ a[1], B, T $ a[2], F, T $ a[3], B, T $ a[4], B, T $ a[5], F] ############################# f[3](0, 0, 0, 0, 0) = [-4] f[3](0, 0, a[3], 0, 0) = [a[3] - 2], 1 <= a[3] f[3](0, 0, 0, 1, 0) = [-2] f[3](0, 0, a[3], 1, 0) = [{[a[3] - 1]}, {[a[3] - 1]}], 1 <= a[3] f[3](0, 0, a[3], a[4], 0) = [{[{[2 a[3] + a[4] - 3]}, {[a[3]]}]}, {[a[3] - 1]}], 2 <= a[4], 0 <= a[3] f[3](1, 0, 0, 0, 0) = [-1] f[3](a[1], 0, 0, 0, 0) = [{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}], 2 <= a[1] f[3](0, 1, 0, 0, 0) = [-2] f[3](a[1], 1, 0, 0, 0) = [a[1] - 1], 1 <= a[1] f[3](0, 2, 0, 0, 0) = [-1/2] f[3](a[1], 2, 0, 0, 0) = [{[a[1]]}, {[a[1]]}], 1 <= a[1] f[3](0, 3, 0, 0, 0) = [{[1/2]}, {[0]}] f[3](a[1], a[2], 0, 0, 0) = [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], 0 <= a[1], 4 <= a[2] f[3](a[1], 3, 0, 0, 0) = [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] , 1 <= a[1] f[3](a[1], 0, a[3], 0, 0) = [a[1] - 3/2 + a[3]], 1 <= a[1], 1 <= a[3] f[3](1, 0, 0, 1, 0) = [{[0]}, {[0]}] f[3](2, 0, 0, 1, 0) = [{[3/2]}, {[3/2]}] f[3](3, 0, 0, 1, 0) = [{[5/2]}, {[5/2]}] f[3](4, 0, 0, 1, 0) = [27/8] f[3](a[1], 0, 0, 1, 0) = [{[a[1] - 1]}, {[{[a[1] - 1]}, {[5]}]}], 5 <= a[1] f[3](a[1], 0, a[3], 1, 0) = [{[a[1] - 1/2 + a[3]]}, {[a[1] - 1/2 + a[3]]}], 1 <= a[1], 1 <= a[3] f[3](1, 0, 0, 2, 0) = [{[5/4]}, {[1/2]}] f[3](2, 0, 0, 2, 0) = [{[{[3]}, {[5/2]}]}, {[3/2]}] f[3](3, 0, 0, 2, 0) = [{[{[5]}, {[7/2]}]}, {[5/2]}] f[3](4, 0, 0, 2, 0) = [{[{[7]}, {[9/2]}]}, {[7/2]}] f[3](5, 0, 0, 2, 0) = [{[{[9]}, {[11/2]}]}, {[9/2]}] f[3](6, 0, 0, 2, 0) = [{[{[11]}, {[{[6]}, {[6]}]}]}, {[11/2]}] f[3](a[1], 0, 0, 2, 0) = [{[a[1]]}, {[a[1] - 1/2]}], 7 <= a[1] f[3](a[1], 0, a[3], 2, 0) = [ {[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}], 1 <= a[1], 1 <= a[3] f[3](a[1], 0, a[3], a[4], 0) = [ {[{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}], 1 <= a[1], 0 <= a[3], 3 <= a[4] f[3](a[1], a[2], a[3], 0, 0) = [a[1] + a[3] - 1], 0 <= a[1], 1 <= a[2], 1 <= a[3] f[3](0, 1, 0, 1, 0) = [-1/2] f[3](a[1], 1, 0, 1, 0) = [{[a[1]]}, {[a[1]]}], 1 <= a[1] f[3](0, 2, 0, 1, 0) = [{[1/2]}, {[0]}] f[3](a[1], 2, 0, 1, 0) = [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] , 1 <= a[1] f[3](a[1], a[2], 0, 1, 0) = [{[{[ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}]}, {[a[1]]}], 3 <= a[2], 0 <= a[1] %1 := {[2 a[1] + a[2] - 2]} f[3](a[1], a[2], a[3], 1, 0) = [{[a[1] + a[3]]}, {[a[1] + a[3]]}], 0 <= a[1], 1 <= a[2], 1 <= a[3] f[3](a[1], a[2], a[3], a[4], 0) = [{ [{[2 a[1] + a[2] + 2 a[3] + a[4] - 3]}, {[a[1] + 1 + a[3]]}]} , {[a[1] + a[3]]}], 2 <= a[4], 0 <= a[1], 0 <= a[3], 1 <= a[2] f[3](0, 0, 0, 0, 1) = [-3] f[3](0, 0, a[3], 0, 1) = [a[3] - 1], 1 <= a[3] f[3](0, 0, a[3], a[4], 1) = [{[2 a[3] + a[4] - 2]}, {[a[3]]}], 0 <= a[3], 1 <= a[4] f[3](1, 0, 0, 0, 1) = [0] f[3](a[1], 0, 0, 0, 1) = [{[a[1] - 1]}, {[{[a[1] - 1]}, {[4]}]}], 2 <= a[1] f[3](0, 1, 0, 0, 1) = [-1] f[3](a[1], 1, 0, 0, 1) = [a[1]], 1 <= a[1] f[3](0, 2, 0, 0, 1) = [1/2] f[3](a[1], 2, 0, 0, 1) = [{[1 + a[1]]}, {[1 + a[1]]}], 1 <= a[1] f[3](a[1], a[2], 0, 0, 1) = [{[ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}], 3 <= a[2], 0 <= a[1] %1 := {[2 a[1] + a[2] - 2]} f[3](a[1], 0, a[3], 0, 1) = [a[1] - 1/2 + a[3]], 1 <= a[1], 1 <= a[3] f[3](1, 0, 0, 1, 1) = [5/4] f[3](2, 0, 0, 1, 1) = [{[3]}, {[5/2]}] f[3](3, 0, 0, 1, 1) = [{[5]}, {[7/2]}] f[3](4, 0, 0, 1, 1) = [{[7]}, {[9/2]}] f[3](a[1], 0, 0, 1, 1) = [{[2 a[1] - 1]}, {[{[a[1]]}, {[6]}]}], 5 <= a[1] f[3](a[1], 0, a[3], 1, 1) = [{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}], 1 <= a[1], 1 <= a[3] f[3](a[1], 0, a[3], a[4], 1) = [{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + a[3] + 1/2]}], 2 <= a[4], 1 <= a[1], 0 <= a[3] f[3](a[1], a[2], a[3], 0, 1) = [a[1] + a[3]], 0 <= a[1], 1 <= a[2], 1 <= a[3] f[3](a[1], a[2], a[3], a[4], 1) = [{[2 a[1] + a[2] + 2 a[3] + a[4] - 2]}, {[a[1] + 1 + a[3]]}], 0 <= a[1], 0 <= a[3], 1 <= a[2], 1 <= a[4] f[3](a[1], a[2], a[3], a[4], a[5]) = [2 a[1] + a[2] + 2 a[3] + a[4] - 1], 0 <= a[2], 0 <= a[1], 0 <= a[3], 2 <= a[5], 0 <= a[4] ############################# Let, f[4], be the value of , [T $ a[1], F, T $ a[2], B, T $ a[3], B, T $ a[4], B, T $ a[5], F] ############################# f[4](0, 0, 0, 0, 0) = [-3] f[4](1, 0, 0, 0, 0) = [{[-1]}, {[-1]}] f[4](a[1], 0, 0, 0, 0) = [a[1] - 1], 2 <= a[1] f[4](a[1], 1, 0, 0, 0) = [{[a[1]]}, {[a[1]]}], 0 <= a[1] f[4](0, a[2], 0, 0, 0) = [{[2 a[2] - 2]}, {[2 a[2] - 2]}], 2 <= a[2] f[4](1, a[2], 0, 0, 0) = [{[2 a[2] - 1]}, {[2 a[2] - 1]}], 2 <= a[2] f[4](2, a[2], 0, 0, 0) = [{[2 a[2]]}, {[2 a[2]]}], 2 <= a[2] f[4](3, a[2], 0, 0, 0) = [{[2 a[2] + 1/2]}, {[2 a[2] + 1/2]}], 2 <= a[2] f[4](a[1], a[2], 0, 0, 0) = [a[1] + 2 a[2] - 3], 2 <= a[2], 4 <= a[1] f[4](0, a[2], a[3], 0, 0) = [2 a[2] + a[3] - 1], 0 <= a[2], 1 <= a[3] f[4](1, a[2], a[3], 0, 0) = [2 a[2] + a[3]], 0 <= a[2], 1 <= a[3] f[4](2, a[2], a[3], 0, 0) = [2 a[2] + a[3] + 1], 0 <= a[2], 1 <= a[3] f[4](3, 0, 1, 0, 0) = [3] f[4](3, a[2], 1, 0, 0) = [2 a[2] + 5/2], 1 <= a[2] f[4](3, a[2], a[3], 0, 0) = [2 a[2] + a[3] + 2], 0 <= a[2], 2 <= a[3] f[4](a[1], 0, 1, 0, 0) = [a[1]], 4 <= a[1] f[4](a[1], a[2], 1, 0, 0) = [{[a[1] + 2 a[2] - 1]}, {[a[1] + 2 a[2] - 1]}], 1 <= a[2], 4 <= a[1] f[4](a[1], a[2], a[3], 0, 0) = [a[1] + 2 a[2] + a[3] - 1], 0 <= a[2], 2 <= a[3], 4 <= a[1] f[4](0, 0, 0, 1, 0) = [-1] f[4](1, 0, 0, 1, 0) = [0] f[4](a[1], 0, 0, 1, 0) = [{[a[1]]}, {[a[1]]}], 2 <= a[1] f[4](a[1], a[2], 0, 1, 0) = [a[1] + 2 a[2] - 1], 0 <= a[1], 1 <= a[2] f[4](0, a[2], 1, 1, 0) = [{[2 a[2] + 1]}, {[2 a[2] + 1]}], 0 <= a[2] f[4](1, a[2], 1, 1, 0) = [{[2 a[2] + 2]}, {[2 a[2] + 2]}], 0 <= a[2] f[4](2, a[2], 1, 1, 0) = [{[2 a[2] + 3]}, {[2 a[2] + 3]}], 0 <= a[2] f[4](3, 0, 1, 1, 0) = [{[4]}, {[4]}] f[4](3, a[2], 1, 1, 0) = [2 a[2] + 15/4], 1 <= a[2] f[4](a[1], 0, 1, 1, 0) = [{[1 + a[1]]}, {[1 + a[1]]}], 4 <= a[1] f[4](a[1], a[2], 1, 1, 0) = [a[1] + 2 a[2]], 1 <= a[2], 4 <= a[1] f[4](a[1], a[2], a[3], 1, 0) = [{[a[1] + 2 a[2] + a[3]]}, {[a[1] + 2 a[2] + a[3]]}], 0 <= a[2], 2 <= a[3], 0 <= a[1] f[4](0, a[2], a[3], 2, 0) = [ {[{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3]]}], 0 <= a[2], 0 <= a[3] f[4](1, a[2], a[3], 2, 0) = [ {[{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 1]}], 0 <= a[2], 0 <= a[3] f[4](2, a[2], a[3], 2, 0) = [ {[{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[2 a[2] + a[3] + 2]}], 0 <= a[2], 0 <= a[3] f[4](3, 0, 0, 2, 0) = [{[{[6]}, {[4]}]}, {[3]}] f[4](3, a[2], 0, 2, 0) = [{[{[3 a[2] + 6]}, {[2 a[2] + 7/2]}]}, {[2 a[2] + 3]}], 1 <= a[2] f[4](3, a[2], a[3], 2, 0) = [ {[{[3 a[2] + 2 a[3] + 6]}, {[2 a[2] + a[3] + 4]}]}, {[2 a[2] + a[3] + 3]}], 0 <= a[2], 1 <= a[3] f[4](a[1], 0, 0, 2, 0) = [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], 4 <= a[1] f[4](a[1], a[2], 0, 2, 0) = [{[a[1] + 2 a[2]]}, {[a[1] + 2 a[2]]}], 1 <= a[2], 4 <= a[1] f[4](a[1], a[2], a[3], 2, 0) = [{ [{[2 a[1] + 3 a[2] + 2 a[3]]}, {[a[1] + 2 a[2] + a[3] + 1]}]} , {[a[1] + 2 a[2] + a[3]]}], 0 <= a[2], 1 <= a[3], 4 <= a[1] f[4](a[1], a[2], a[3], a[4], 0) = [{[ {[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 2]}, {[a[1] + 2 a[2] + a[3] + 1]}]}, {[a[1] + 2 a[2] + a[3]]}], 0 <= a[2], 0 <= a[1], 0 <= a[3], 3 <= a[4] f[4](0, 0, 0, 0, 1) = [-2] f[4](1, 0, 0, 0, 1) = [{[0]}, {[0]}] f[4](a[1], 0, 0, 0, 1) = [a[1]], 2 <= a[1] f[4](a[1], 1, 0, 0, 1) = [{[1 + a[1]]}, {[1 + a[1]]}], 0 <= a[1] f[4](0, a[2], 0, 0, 1) = [{[2 a[2] - 1]}, {[2 a[2] - 1]}], 2 <= a[2] f[4](1, a[2], 0, 0, 1) = [{[2 a[2]]}, {[2 a[2]]}], 2 <= a[2] f[4](2, a[2], 0, 0, 1) = [{[2 a[2] + 1]}, {[2 a[2] + 1]}], 2 <= a[2] f[4](3, a[2], 0, 0, 1) = [{[2 a[2] + 3/2]}, {[2 a[2] + 3/2]}], 2 <= a[2] f[4](a[1], a[2], 0, 0, 1) = [a[1] + 2 a[2] - 2], 2 <= a[2], 4 <= a[1] f[4](0, a[2], a[3], 0, 1) = [2 a[2] + a[3]], 0 <= a[2], 1 <= a[3] f[4](1, a[2], a[3], 0, 1) = [2 a[2] + a[3] + 1], 0 <= a[2], 1 <= a[3] f[4](2, a[2], a[3], 0, 1) = [2 a[2] + a[3] + 2], 0 <= a[2], 1 <= a[3] f[4](3, 0, 1, 0, 1) = [4] f[4](3, a[2], 1, 0, 1) = [2 a[2] + 7/2], 1 <= a[2] f[4](3, a[2], a[3], 0, 1) = [2 a[2] + a[3] + 3], 0 <= a[2], 2 <= a[3] f[4](a[1], 0, 1, 0, 1) = [1 + a[1]], 4 <= a[1] f[4](a[1], a[2], 1, 0, 1) = [{[a[1] + 2 a[2]]}, {[a[1] + 2 a[2]]}], 1 <= a[2], 4 <= a[1] f[4](a[1], a[2], a[3], 0, 1) = [a[1] + 2 a[2] + a[3]], 0 <= a[2], 2 <= a[3], 0 <= a[1] f[4](a[1], 0, 0, 1, 1) = [{[2 a[1]]}, {[1 + a[1]]}], 0 <= a[1] f[4](a[1], a[2], 0, 1, 1) = [{[2 a[1] + 3 a[2]]}, {[{[a[1] + 2 a[2]]}, {[2 a[2] + 4]}]}], 0 <= a[1], 1 <= a[2] f[4](a[1], a[2], a[3], 1, 1) = [{[2 a[1] + 3 a[2] + 2 a[3]]}, {[a[1] + 2 a[2] + a[3] + 1]}], 0 <= a[2], 0 <= a[1], 1 <= a[3] f[4](a[1], a[2], a[3], a[4], 1) = [ {[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}, {[a[1] + 2 a[2] + a[3] + 1]}], 0 <= a[2], 2 <= a[4], 0 <= a[1], 0 <= a[3] f[4](a[1], a[2], a[3], a[4], a[5]) = [2 a[1] + 3 a[2] + 2 a[3] + a[4]], 0 <= a[2], 0 <= a[1], 0 <= a[3], 2 <= a[5], 0 <= a[4] ############################# Let, f[5], be the value of , [T $ a[1], B, T $ a[2], B, T $ a[3], F, T $ a[4], F, B] ############################# f[5](0, 0, 0, 0) = [-4] f[5](1, 0, 0, 0) = [-1] f[5](a[1], 0, 0, 0) = [{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}], 2 <= a[1] f[5](0, 1, 0, 0) = [{[-1]}, {[-1]}] f[5](a[1], 1, 0, 0) = [{[a[1] - 1/2]}, {[{[a[1] - 1]}, {[{[a[1] - 1]}, {[3]}]}]}], 1 <= a[1] f[5](0, 2, 0, 0) = [{[1/4]}, {[-1/4]}] f[5](a[1], 2, 0, 0) = [{[{[2 a[1]]}, {[a[1] + 1/2]}]}, {[{[{[a[1]]}, {[a[1]]}]}, {[a[1]]}]}], 1 <= a[1] f[5](a[1], a[2], 0, 0) = [ {[{[2 a[1] + a[2] - 2]}, {[a[1] + 1/2]}]}, {[ {[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}]}], 3 <= a[2], 0 <= a[1] f[5](0, 0, 0, a[4]) = [-2], 1 <= a[4] f[5](a[1], 0, 0, a[4]) = [a[1] - 1], 1 <= a[1], 1 <= a[4] f[5](0, 1, 0, a[4]) = [-1/2], 1 <= a[4] f[5](a[1], 1, 0, a[4]) = [{[a[1]]}, {[a[1]]}], 1 <= a[1], 1 <= a[4] f[5](a[1], a[2], 0, a[4]) = [{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}], 2 <= a[2], 0 <= a[1], 1 <= a[4] f[5](0, 0, 1, 0) = [-1] f[5](a[1], 0, 1, 0) = [a[1] - 1/2], 1 <= a[1] f[5](a[1], a[2], 1, 0) = [{[2 a[1] + a[2] - 1]}, {[a[1] + 1/2]}], 0 <= a[1], 1 <= a[2] f[5](0, 0, 1, a[4]) = [-1], 1 <= a[4] f[5](a[1], 0, 1, a[4]) = [a[1]], 1 <= a[1], 1 <= a[4] f[5](a[1], a[2], 1, a[4]) = [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}], 0 <= a[1], 1 <= a[2], 1 <= a[4] f[5](a[1], a[2], a[3], a[4]) = [2 a[1] + a[2]], 0 <= a[2], 2 <= a[3], 0 <= a[1], 0 <= a[4] ############################# Let, f[6], be the value of , [T $ a[1], B, T $ a[2], F, T $ a[3], B, T $ a[4], F, B] ############################# f[6](0, 0, 0, 0) = [-3] f[6](1, 0, 0, 0) = [{[-1]}, {[-1]}] f[6](a[1], 0, 0, 0) = [{[a[1] - 2]}, {[3]}], 2 <= a[1] f[6](0, 0, a[3], 0) = [{[a[3] - 2]}, {[a[3] - 2]}], 1 <= a[3] f[6](a[1], 0, a[3], 0) = [a[1] + a[3] - 1], 1 <= a[1], 1 <= a[3] f[6](0, 1, 0, 0) = [-1] f[6](a[1], 1, 0, 0) = [{[a[1] - 1]}, {[{[a[1] - 1]}, {[3]}]}], 1 <= a[1] f[6](0, 2, 0, 0) = [-1/4] f[6](a[1], 2, 0, 0) = [{[{[a[1]]}, {[a[1]]}]}, {[a[1]]}], 1 <= a[1] f[6](a[1], a[2], 0, 0) = [ {[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}], 3 <= a[2], 0 <= a[1] f[6](a[1], a[2], a[3], 0) = [a[1] - 1/2 + a[3]], 0 <= a[1], 1 <= a[2], 1 <= a[3] f[6](0, 0, a[3], a[4]) = [a[3] - 1], 0 <= a[3], 1 <= a[4] f[6](1, 0, 0, 1) = [1/2] f[6](2, 0, 0, 1) = [3/2] f[6](3, 0, 0, 1) = [5/2] f[6](4, 0, 0, 1) = [7/2] f[6](a[1], 0, 0, 1) = [{[a[1] - 1]}, {[5]}], 5 <= a[1] f[6](a[1], 0, a[3], 1) = [a[1] - 1/2 + a[3]], 1 <= a[1], 1 <= a[3] f[6](a[1], 0, a[3], a[4]) = [a[1] - 1/2 + a[3]], 2 <= a[4], 1 <= a[1], 0 <= a[3] f[6](a[1], a[2], a[3], a[4]) = [a[1] + a[3]], 0 <= a[1], 0 <= a[3], 1 <= a[2], 1 <= a[4] ############################# Let, f[7], be the value of , [T $ a[1], F, T $ a[2], B, T $ a[3], B, T $ a[4], F, B] ############################# f[7](0, 0, 0, 0) = [-2] f[7](1, 0, 0, 0) = [-1] f[7](a[1], 0, 0, 0) = [{[a[1] - 1]}, {[a[1] - 1]}], 2 <= a[1] f[7](a[1], 1, 0, 0) = [{[{[a[1]]}, {[a[1]]}]}, {[3]}], 0 <= a[1] f[7](a[1], a[2], 0, 0) = [{[a[1] + 2 a[2] - 3]}, {[2 a[2] + 1]}], 2 <= a[2], 0 <= a[1] f[7](a[1], 0, 1, 0) = [{[a[1]]}, {[a[1]]}], 0 <= a[1] f[7](0, a[2], 1, 0) = [{[2 a[2]]}, {[2 a[2]]}], 1 <= a[2] f[7](1, a[2], 1, 0) = [{[2 a[2] + 1]}, {[2 a[2] + 1]}], 1 <= a[2] f[7](2, a[2], 1, 0) = [{[2 a[2] + 2]}, {[2 a[2] + 2]}], 1 <= a[2] f[7](3, a[2], 1, 0) = [{[2 a[2] + 5/2]}, {[2 a[2] + 5/2]}], 1 <= a[2] f[7](a[1], a[2], 1, 0) = [a[1] + 2 a[2] - 1], 1 <= a[2], 4 <= a[1] f[7](a[1], a[2], a[3], 0) = [{[a[1] + 2 a[2] + a[3] - 1]}, {[a[1] + 2 a[2] + a[3] - 1]}], 0 <= a[2], 2 <= a[3], 0 <= a[1] f[7](a[1], 0, 0, 1) = [a[1]], 0 <= a[1] f[7](a[1], a[2], 0, 1) = [{[a[1] + 2 a[2] - 1]}, {[2 a[2] + 3]}], 0 <= a[1], 1 <= a[2] f[7](a[1], a[2], a[3], 1) = [a[1] + 2 a[2] + a[3]], 0 <= a[2], 0 <= a[1], 1 <= a[3] f[7](a[1], a[2], a[3], a[4]) = [a[1] + 2 a[2] + a[3]], 0 <= a[2], 2 <= a[4], 0 <= a[1], 0 <= a[3] ############################# Let, f[8], be the value of , [T $ a[1], B, T $ a[2], F, T $ a[3], F, B, B] ############################# f[8](0, 0, a[3]) = [a[3] - 2], 0 <= a[3] f[8](1, 0, 0) = [{[0]}, {[-1/2]}] f[8](2, 0, 0) = [{[1]}, {[1]}] f[8](3, 0, 0) = [{[2]}, {[2]}] f[8](4, 0, 0) = [11/4] f[8](a[1], 0, 0) = [3], 5 <= a[1] f[8](a[1], 0, a[3]) = [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}], 1 <= a[1], 1 <= a[3] f[8](a[1], 1, 0) = [{[a[1] - 1]}, {[3]}], 0 <= a[1] f[8](a[1], 1, a[3]) = [a[1] + a[3]], 0 <= a[1], 1 <= a[3] f[8](a[1], a[2], a[3]) = [a[1] + a[3]], 2 <= a[2], 0 <= a[1], 0 <= a[3] ############################# Let, f[9], be the value of , [T $ a[1], F, T $ a[2], B, T $ a[3], F, B, B] ############################# f[9](0, 0, 0) = [-1] f[9](1, 0, 0) = [-1/2] f[9](a[1], 0, 0) = [{[{[a[1] - 1]}, {[a[1] - 1]}]}, {[0]}], 2 <= a[1] f[9](a[1], 1, 0) = [{[{[{[a[1]]}, {[a[1]]}]}, {[3]}]}, {[2]}], 0 <= a[1] f[9](a[1], a[2], 0) = [{[{[a[1] + 2 a[2] - 3]}, {[2 a[2] + 1]}]}, {[2 a[2]]}], 2 <= a[2], 0 <= a[1] f[9](a[1], 0, 1) = [{[{[a[1]]}, {[a[1]]}]}, {[3]}], 0 <= a[1] f[9](a[1], a[2], 1) = [{[a[1] + 2 a[2] - 1]}, {[2 a[2] + 3]}], 0 <= a[1], 1 <= a[2] f[9](a[1], a[2], a[3]) = [a[1] + 2 a[2] + a[3] - 1], 0 <= a[2], 2 <= a[3], 0 <= a[1] ############################# Let, f[10], be the value of , [T $ a[1], F, T $ a[2], F, B, B, B] ############################# f[10](a[1], a[2]) = [2 a[2]], 0 <= a[2], 0 <= a[1] Now we will prove by applying induction to each of the above conjectures one by one. If everythings are true, we get the proofs. ############### ##Begin to prove## ############### ########## #, f[1], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{}, {f[2](0, 0, 0, 0, 0)}] = , [{}, {[-5]}] = , [-6] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[1](0, 1, 0, 0, 0)}, {f[2](1, 0, 0, 0, 0)}] = , [{[-2]}, {[-2]}] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 1, 0, 0, 0)}, {f[2](a[1], 0, 0, 0, 0)}] = , [{[a[1] - 2]}, {[a[1] - 2]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[1](0, 0, 1, 0, 0)}, {f[2](0, 1, 0, 0, 0)}] = , [{[-3]}, {[{[-2]}, {[-2]}]}] = , [-2] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [ {f[1](a[1] - 1, 2, 0, 0, 0), f[1](a[1], 0, 1, 0, 0)}, {f[2](a[1], 1, 0, 0, 0)}] = , [{[{[2 a[1] - 3]}, {[a[1] - 1]}]}, {[{[a[1] - 1]}, {[a[1] - 1]}]}] = , [a[1] - 1] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[1](a[1] - 1, 3, 0, 0, 0), f[1](a[1], 1, 1, 0, 0)}, {f[2](a[1], 2, 0, 0, 0)}] = , [{[2 a[1] - 1], [{[2 a[1] - 3/2]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[2 a[1] - 1]}, {[a[1]]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 2} The value of the game = , [{f[1](0, 1, 1, 0, 0)}, {f[2](0, 2, 0, 0, 0)}] = , [{[-1]}, {[{[-1/2]}, {[-1/2]}]}] = , [-1/2] For the domain, {3 <= a[2], a[3] = 0, a[4] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 0, 0), f[1](a[1], a[2] - 1, 1, 0, 0)}, {f[2](a[1], a[2], 0, 0, 0)}] = , [{[{[2 a[1] - 7/2 + a[2]]}, {[a[1] - 1]}], [2 a[1] + a[2] - 5/2]}, {[a[1]]}] = , [{[2 a[1] + a[2] - 5/2]}, {[a[1]]}] For the domain, {3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[1](0, a[2] - 1, 1, 0, 0)}, {f[2](0, a[2], 0, 0, 0)}] = , [{[- 5/2 + a[2]]}, {[0]}] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[1](0, 0, 0, 1, 0)}, {f[2](0, 0, 1, 0, 0)}] = , [{[-4]}, {[-2]}] = , [-3] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[1](1, 0, 0, 1, 0), f[1](0, 1, 1, 0, 0)}, {f[2](1, 0, 1, 0, 0)}] = , [{[-1]}, {[0]}] = , [-1/2] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [ {f[1](a[1] - 1, 1, 1, 0, 0), f[1](a[1], 0, 0, 1, 0)}, {f[2](a[1], 0, 1, 0, 0)}] = , [{[2 a[1] - 3], [a[1] - 1]}, {[a[1] - 1]}] = , [{[2 a[1] - 3]}, {[a[1] - 1]}] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{ f[1](1, 0, 2, 0, 0), f[1](1, 1, 0, 1, 0), f[1](0, 2, 1, 0, 0) }, {f[2](1, 1, 1, 0, 0)}] = , [{[1/2], [{[1]}, {[1]}]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [{f[1](a[1], 0, 2, 0, 0), f[1](a[1], 1, 0, 1, 0), f[1](a[1] - 1, 2, 1, 0, 0)}, {f[2](a[1], 1, 1, 0, 0)}] = , [{[{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}], [2 a[1] - 3/2]}, {[{[2 a[1] - 1]}, {[a[1]]}]}] = , [2 a[1] - 1] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[1](0, 0, 2, 0, 0), f[1](0, 1, 0, 1, 0)}, {f[2](0, 1, 1, 0, 0)}] = , [{[{[-1]}, {[-1]}]}, {[{[-1]}, {[0]}]}] = , [-1] For the domain, {a[3] = 1, 3 <= a[2], a[4] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 1, 0, 0), f[1](a[1], a[2] - 1, 2, 0, 0), f[1](a[1], a[2], 0, 1, 0)}, {f[2](a[1], a[2], 1, 0, 0)}] = , [{[2 a[1] + a[2] - 2], [ {[{[2 a[1] + a[2] - 2]}, {[2 a[1] + a[2] - 2]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], [2 a[1] + a[2] - 5/2]}, {[{[2 a[1] + a[2] - 3/2]}, {[a[1]]}]}] = , [2 a[1] + a[2] - 3/2] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [{f[1](a[1], 1, 2, 0, 0), f[1](a[1], 2, 0, 1, 0), f[1](a[1] - 1, 3, 1, 0, 0)}, {f[2](a[1], 2, 1, 0, 0)}] = , [{[2 a[1]], [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], [2 a[1] - 1/2]}, {[{[2 a[1] + 1/2]}, {[a[1]]}]}] = , [2 a[1] + 1/2] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 2} The value of the game = , [ {f[1](0, 1, 2, 0, 0), f[1](0, 2, 0, 1, 0)}, {f[2](0, 2, 1, 0, 0)}] = , [{[{[1/2]}, {[1/2]}]}, {[{[1/2]}, {[0]}]}] = , [1/2] For the domain, {a[3] = 1, 3 <= a[2], a[1] = 0, a[4] = 0, a[5] = 0} The value of the game = , [ {f[1](0, a[2] - 1, 2, 0, 0), f[1](0, a[2], 0, 1, 0)}, {f[2](0, a[2], 1, 0, 0)}] = , [{[-2 + a[2]], [{[{[-2 + a[2]]}, {[-2 + a[2]]}]}, {[{[1]}, {[1]}]}]}, {[{[- 3/2 + a[2]]}, {[0]}]}] = , [- 3/2 + a[2]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 2} The value of the game = , [{f[1](0, 0, 1, 1, 0)}, {f[2](0, 0, 2, 0, 0)}] = , [{[{[0]}, {[{[-1]}, {[-1]}]}]}, {[-1]}] = , [{[-1]}, {[-1]}] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1, a[3] = 2} The value of the game = , [ {f[1](0, 1, 2, 0, 0), f[1](1, 0, 1, 1, 0)}, {f[2](1, 0, 2, 0, 0)}] = , [{[{[1/2]}, {[1/2]}], [{[3]}, {[{[1]}, {[1]}]}]}, {[1]}] = , [{[1]}, {[1]}] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, 2 <= a[1], a[3] = 2} The value of the game = , [ {f[1](a[1] - 1, 1, 2, 0, 0), f[1](a[1], 0, 1, 1, 0)}, {f[2](a[1], 0, 2, 0, 0)}] = , [{[2 a[1] - 2], [{[3 a[1]]}, {[ {[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}]}]}, {[2 a[1] - 1]}] = , [2 a[1] - 3/2] For the domain, {a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 1, a[3] = 2} The value of the game = , [ {f[1](0, 0, 3, 0, 0), f[1](0, 1, 1, 1, 0)}, {f[2](0, 1, 2, 0, 0)}] = , [{[{[0]}, {[0]}], [{[2]}, {[{[1/2]}, {[1/2]}]}]}, {[1/2]}] = , [{[1/2]}, {[1/2]}] For the domain, {a[4] = 0, a[5] = 0, a[2] = 1, 1 <= a[1], a[3] = 2} The value of the game = , [{f[1](a[1] - 1, 2, 2, 0, 0), f[1](a[1], 0, 3, 0, 0), f[1](a[1], 1, 1, 1, 0)}, {f[2](a[1], 1, 2, 0, 0)}] = , [{[2 a[1] - 1], [{[2 a[1]]}, {[2 a[1]]}], [{[3 a[1] + 2]}, { [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} ]}, {[2 a[1] + 1/2]}] = , [2 a[1]] For the domain, {2 <= a[2], a[4] = 0, a[5] = 0, 1 <= a[1], a[3] = 2} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 2, 0, 0), f[1](a[1], a[2] - 1, 3, 0, 0), f[1](a[1], a[2], 1, 1, 0)}, {f[2](a[1], a[2], 2, 0, 0)}] = , [{[2 a[1] + a[2] - 2], [{[3 a[1] + 2 a[2]]}, {[{[%1, %1]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}], [%1, %1]}, {[2 a[1] + a[2] - 1/2]}] %1 := {[2 a[1] + a[2] - 1]} = , [2 a[1] + a[2] - 1] For the domain, {2 <= a[2], a[1] = 0, a[4] = 0, a[5] = 0, a[3] = 2} The value of the game = , [ {f[1](0, a[2] - 1, 3, 0, 0), f[1](0, a[2], 1, 1, 0)}, {f[2](0, a[2], 2, 0, 0)}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}], [{[2 a[2]]}, {[{[{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[1]}, {[1]}]}]}]}, {[- 1/2 + a[2]]}] = , [a[2] - 1] For the domain, {a[4] = 0, a[5] = 0, 1 <= a[1], 1 <= a[2], a[3] = 3} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 3, 0, 0), f[1](a[1], a[2] - 1, 4, 0, 0), f[1](a[1], a[2], 2, 1, 0)}, {f[2](a[1], a[2], 3, 0, 0)}] = , [{[{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}], [{[3 a[1] + 2 a[2] + 1]}, {[%1, %1]}]}, {[ {[{[{[3 a[1] + 2 a[2]]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, %1]} , %1]}] %1 := {[2 a[1] + a[2]]} = , [{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}] For the domain, {a[4] = 0, a[5] = 0, 1 <= a[1], 1 <= a[2], 4 <= a[3]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, a[3], 0, 0), f[1](a[1], a[2] - 1, a[3] + 1, 0, 0), f[1](a[1], a[2], a[3] - 1, 1, 0)}, {f[2](a[1], a[2], a[3], 0, 0)}] = , [{[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[%1, %1]}], [{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[{[ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[2 a[1] + a[2] + 1/2]}]}, %1]}, %1]}] %1 := {[2 a[1] + a[2]]} = , [{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], a[3] = 3} The value of the game = , [ {f[1](a[1] - 1, 1, 3, 0, 0), f[1](a[1], 0, 2, 1, 0)}, {f[2](a[1], 0, 3, 0, 0)}] = , [{[{[2 a[1] - 1]}, {[2 a[1] - 1]}], [{[3 a[1] + 1]}, {[{[2 a[1]]}, {[2 a[1]]}]}]}, {[{[{[2 a[1]]}, {[2 a[1]]}]}, {[2 a[1]]}]}] = , [{[2 a[1]]}, {[2 a[1]]}] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], 4 <= a[3]} The value of the game = , [{ f[1](a[1] - 1, 1, a[3], 0, 0), f[1](a[1], 0, a[3] - 1, 1, 0)} , {f[2](a[1], 0, a[3], 0, 0)}] = , [{[{[2 a[1] - 1]}, {[2 a[1] - 1]}], [{[3 a[1] - 2 + a[3]]}, {[{[2 a[1]]}, {[2 a[1]]}]}]}, {[ {[{[{[3 a[1] - 3 + a[3]]}, {[2 a[1] + 1/2]}]}, {[2 a[1]]}]}, {[2 a[1]]}]}] = , [{[2 a[1]]}, {[2 a[1]]}] For the domain, {a[1] = 0, a[4] = 0, a[5] = 0, 1 <= a[2], a[3] = 3} The value of the game = , [ {f[1](0, a[2] - 1, 4, 0, 0), f[1](0, a[2], 2, 1, 0)}, {f[2](0, a[2], 3, 0, 0)}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}], [{[2 a[2] + 1]}, {[{[a[2]]}, {[a[2]]}]}]}, {[{ [{[{[2 a[2]]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}]}, {[a[2]]}] }, {[a[2]]}]}] = , [{[a[2]]}, {[a[2]]}] For the domain, {a[1] = 0, a[4] = 0, a[5] = 0, 1 <= a[2], 4 <= a[3]} The value of the game = , [{f[1](0, a[2], a[3] - 1, 1, 0), f[1](0, a[2] - 1, a[3] + 1, 0, 0)}, {f[2](0, a[2], a[3], 0, 0)}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}], [{[-2 + 2 a[2] + a[3]]}, {[{[a[2]]}, {[a[2]]}]}]}, {[ {[{[{[-3 + 2 a[2] + a[3]]}, {[1/2 + a[2]]}]}, {[a[2]]}]}, {[a[2]]}]}] = , [{[a[2]]}, {[a[2]]}] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 3} The value of the game = , [{f[1](0, 0, 2, 1, 0)}, {f[2](0, 0, 3, 0, 0)}] = , [{[{[1]}, {[{[0]}, {[0]}]}]}, {[{[{[0]}, {[0]}]}, {[0]}]}] = , [{[0]}, {[0]}] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, 4 <= a[3]} The value of the game = , [{f[1](0, 0, a[3] - 1, 1, 0)}, {f[2](0, 0, a[3], 0, 0)}] = , [{[{[a[3] - 2]}, {[{[0]}, {[0]}]}]}, {[{[{[{[a[3] - 3]}, {[1/2]}]}, {[0]}]}, {[0]}]}] = , [{[0]}, {[0]}] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{}, {f[2](0, 0, 0, 1, 0)}] = , [{}, {[-3]}] = , [-4] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[1](0, 1, 0, 1, 0)}, {f[2](1, 0, 0, 1, 0)}] = , [{[{[-1]}, {[-1]}]}, {[-1/2]}] = , [-1] For the domain, {a[4] = 1, a[1] = 2, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{f[1](1, 1, 0, 1, 0)}, {f[2](2, 0, 0, 1, 0)}] = , [{[{[1]}, {[1]}]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, 3 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 1, 0, 1, 0)}, {f[2](a[1], 0, 0, 1, 0)}] = , [{[{[{[{[2 a[1] - 4]}, {[2 a[1] - 4]}]}, {[a[1] - 1/2]}]}, {[a[1] - 1]}]}, {[{[a[1] - 1]}, {[a[1] - 1]}]}] = , [a[1] - 1] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[1](0, 0, 1, 1, 0)}, {f[2](0, 1, 0, 1, 0)}] = , [{[{[0]}, {[{[-1]}, {[-1]}]}]}, {[-1]}] = , [{[-1]}, {[-1]}] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[1](0, 2, 0, 1, 0), f[1](1, 0, 1, 1, 0)}, {f[2](1, 1, 0, 1, 0)}] = , [{[{[1/2]}, {[1/2]}], [{[3]}, {[{[1]}, {[1]}]}]}, {[1]}] = , [{[1]}, {[1]}] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[1](a[1] - 1, 2, 0, 1, 0), f[1](a[1], 0, 1, 1, 0)}, {f[2](a[1], 1, 0, 1, 0)}] = , [{[{[3 a[1]]}, {[{[{[%1, %1]}, {[a[1] + 1/2]}]}, {[a[1]]}]}], [{[%1, %1]}, {[{[a[1]]}, {[a[1]]}]}]}, {[a[1]]}] %1 := {[2 a[1] - 2]} = , [{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 2} The value of the game = , [{f[1](0, 1, 1, 1, 0)}, {f[2](0, 2, 0, 1, 0)}] = , [{[{[2]}, {[{[1/2]}, {[1/2]}]}]}, {[1/2]}] = , [{[1/2]}, {[1/2]}] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[1](a[1] - 1, 3, 0, 1, 0), f[1](a[1], 1, 1, 1, 0)}, {f[2](a[1], 2, 0, 1, 0)}] = , [{[{[3 a[1] + 2]}, { [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} ], [{[{[2 a[1] - 1]}, {[2 a[1] - 1]}]}, {[{[a[1]]}, {[a[1]]}]}]} , {[{[1 + a[1]]}, {[1 + a[1]]}]}] = , [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] For the domain, {a[4] = 1, 3 <= a[2], a[3] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 1, 0), f[1](a[1], a[2] - 1, 1, 1, 0)}, {f[2](a[1], a[2], 0, 1, 0)}] = , [{[{[3 a[1] + 2 a[2] - 2]}, {[ {[{[2 a[1] + a[2] - 2]}, {[2 a[1] + a[2] - 2]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}], [ {[{[2 a[1] + a[2] - 3]}, {[2 a[1] + a[2] - 3]}]}, {[{[a[1]]}, {[a[1]]}]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] = , [{[{[2 a[1] + a[2] - 2]}, {[2 a[1] + a[2] - 2]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] For the domain, {a[4] = 1, 3 <= a[2], a[1] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{f[1](0, a[2] - 1, 1, 1, 0)}, {f[2](0, a[2], 0, 1, 0)}] = , [{[{[2 a[2] - 2]}, {[{[{[-2 + a[2]]}, {[-2 + a[2]]}]}, {[{[1]}, {[1]}]}]}]}, {[{[1]}, {[1]}]}] = , [{[{[-2 + a[2]]}, {[-2 + a[2]]}]}, {[{[1]}, {[1]}]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [{f[1](0, 0, 0, 2, 0)}, {f[2](0, 0, 1, 1, 0)}] = , [{[0]}, {[{[-1]}, {[-1]}]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[1](0, 1, 1, 1, 0), f[1](1, 0, 0, 2, 0)}, {f[2](1, 0, 1, 1, 0)}] = , [{[{[2]}, {[{[1/2]}, {[1/2]}]}], [3]}, {[{[1]}, {[1]}]}] = , [{[3]}, {[{[1]}, {[1]}]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [ {f[1](a[1] - 1, 1, 1, 1, 0), f[1](a[1], 0, 0, 2, 0)}, {f[2](a[1], 0, 1, 1, 0)}] = , [{[{[3 a[1] - 1]}, {[{[%1, %1]}, {[{[a[1]]}, {[a[1]]}]}]}], [3 a[1]]}, {[{[{[%1, %1]}, {[a[1] + 1/2]}]}, {[a[1]]}]}] %1 := {[2 a[1] - 2]} = , [{[3 a[1]]}, {[ {[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[1](0, 0, 2, 1, 0), f[1](0, 1, 0, 2, 0)}, {f[2](0, 1, 1, 1, 0)}] = , [{[2], [{[1]}, {[{[0]}, {[0]}]}]}, {[{[1/2]}, {[1/2]}]}] = , [{[2]}, {[{[1/2]}, {[1/2]}]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 2, 1, 1, 0), f[1](a[1], 0, 2, 1, 0), f[1](a[1], 1, 0, 2, 0)}, {f[2](a[1], 1, 1, 1, 0)}] = , [{[{[3 a[1] + 1]}, { [{[{[2 a[1] - 1]}, {[2 a[1] - 1]}]}, {[{[a[1]]}, {[a[1]]}]}]} ], [3 a[1] + 2], [{[3 a[1] + 1]}, {[{[2 a[1]]}, {[2 a[1]]}]}] }, { [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} ] = , [{[3 a[1] + 2]}, { [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} ] For the domain, {a[3] = 1, a[4] = 1, 2 <= a[2], a[5] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 1, 1, 0), f[1](a[1], a[2] - 1, 2, 1, 0), f[1](a[1], a[2], 0, 2, 0)}, {f[2](a[1], a[2], 1, 1, 0)}] = , [{[{[3 a[1] - 1 + 2 a[2]]}, {[ {[{[2 a[1] + a[2] - 2]}, {[2 a[1] + a[2] - 2]}]}, {[{[a[1]]}, {[a[1]]}]}]}], [3 a[1] + 2 a[2]], [{[3 a[1] - 1 + 2 a[2]]}, {[%1, %1]}]}, {[{[%1, %1]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}] %1 := {[2 a[1] + a[2] - 1]} = , [{[3 a[1] + 2 a[2]]}, {[ {[{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}] For the domain, {a[3] = 1, a[4] = 1, 2 <= a[2], a[1] = 0, a[5] = 0} The value of the game = , [ {f[1](0, a[2] - 1, 2, 1, 0), f[1](0, a[2], 0, 2, 0)}, {f[2](0, a[2], 1, 1, 0)}] = , [{[2 a[2]], [{[2 a[2] - 1]}, {[{[a[2] - 1]}, {[a[2] - 1]}]}]}, {[{[{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[1]}, {[1]}]}]}] = , [{[2 a[2]]}, {[{[{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[1]}, {[1]}]}]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, a[3], 1, 0), f[1](a[1], a[2] - 1, a[3] + 1, 1, 0), f[1](a[1], a[2], a[3] - 1, 2, 0)}, {f[2](a[1], a[2], a[3], 1, 0)}] = , [{[3 a[1] + 2 a[2] + a[3] - 1], [ {[3 a[1] + 2 a[2] + a[3] - 2]}, {[{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}]}, {[{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}]}] = , [{[3 a[1] + 2 a[2] + a[3] - 1]}, {[{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}]}] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{ f[1](a[1] - 1, 1, a[3], 1, 0), f[1](a[1], 0, a[3] - 1, 2, 0)} , {f[2](a[1], 0, a[3], 1, 0)}] = , [{[3 a[1] - 1 + a[3]], [{[3 a[1] - 2 + a[3]]}, {[{[2 a[1] - 1]}, {[2 a[1] - 1]}]}]}, {[{[2 a[1]]}, {[2 a[1]]}]}] = , [{[3 a[1] - 1 + a[3]]}, {[{[2 a[1]]}, {[2 a[1]]}]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[1](0, a[2] - 1, a[3] + 1, 1, 0), f[1](0, a[2], a[3] - 1, 2, 0)}, {f[2](0, a[2], a[3], 1, 0)}] = , [{[2 a[2] + a[3] - 1], [{[-2 + 2 a[2] + a[3]]}, {[{[a[2] - 1]}, {[a[2] - 1]}]}]}, {[{[a[2]]}, {[a[2]]}]}] = , [{[2 a[2] + a[3] - 1]}, {[{[a[2]]}, {[a[2]]}]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [{f[1](0, 0, a[3] - 1, 2, 0)}, {f[2](0, 0, a[3], 1, 0)}] = , [{[a[3] - 1]}, {[{[0]}, {[0]}]}] For the domain, {2 <= a[4], a[5] = 0, 1 <= a[1], 1 <= a[2], 1 <= a[3]} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], 0), f[1](a[1], a[2] - 1, a[3] + 1, a[4], 0), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 0)}, {}] = , [{[3 a[1] + 2 a[2] + a[3] - 1]}, {}] = , [3 a[1] + 2 a[2] + a[3]] For the domain, {2 <= a[4], a[3] = 0, a[5] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, a[4], 0), f[1](a[1], a[2] - 1, 1, a[4], 0)}, {}] = , [{[3 a[1] + 2 a[2] - 1]}, {}] = , [3 a[1] + 2 a[2]] For the domain, {2 <= a[4], a[2] = 0, a[5] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[1](a[1], 0, a[3] - 1, a[4] + 1, 0), f[1](a[1] - 1, 1, a[3], a[4], 0)}, {}] = , [{[3 a[1] - 1 + a[3]]}, {}] = , [3 a[1] + a[3]] For the domain, {2 <= a[4], a[2] = 0, a[3] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 1, 0, a[4], 0)}, {}] = , [{[3 a[1] - 1]}, {}] = , [3 a[1]] For the domain, {2 <= a[4], a[1] = 0, a[5] = 0, 1 <= a[2], 1 <= a[3]} The value of the game = , [{f[1](0, a[2] - 1, a[3] + 1, a[4], 0), f[1](0, a[2], a[3] - 1, a[4] + 1, 0)}, {}] = , [{[2 a[2] + a[3] - 1]}, {}] = , [2 a[2] + a[3]] For the domain, {2 <= a[4], a[1] = 0, a[3] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], 0)}, {}] = , [{[2 a[2] - 1]}, {}] = , [2 a[2]] For the domain, {2 <= a[4], a[1] = 0, a[2] = 0, a[5] = 0, 1 <= a[3]} The value of the game = , [{f[1](0, 0, a[3] - 1, a[4] + 1, 0)}, {}] = , [{[a[3] - 1]}, {}] = , [a[3]] For the domain, {2 <= a[4], a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{}, {}] = , [{}, {}] = , [0] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{}, {f[2](0, 0, 0, 0, 1)}] = , [{}, {[-4]}] = , [-5] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[1](0, 1, 0, 0, 1)}, {f[2](1, 0, 0, 0, 1)}] = , [{[-1]}, {[-1]}] For the domain, {a[5] = 1, a[1] = 2, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[1](1, 1, 0, 0, 1)}, {f[2](2, 0, 0, 0, 1)}] = , [{[1]}, {[1]}] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, 3 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 1, 0, 0, 1)}, {f[2](a[1], 0, 0, 0, 1)}] = , [{[{[{[2 a[1] - 4]}, {[2 a[1] - 4]}]}, {[a[1] - 1/2]}]}, {[a[1] - 1]}] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[1](0, 0, 1, 0, 1)}, {f[2](0, 1, 0, 0, 1)}] = , [{[-3/2]}, {[{[-1]}, {[-1]}]}] = , [-1] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[1](0, 2, 0, 0, 1), f[1](1, 0, 1, 0, 1)}, {f[2](1, 1, 0, 0, 1)}] = , [{[1/2], [{[0]}, {[1]}]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[1](a[1] - 1, 2, 0, 0, 1), f[1](a[1], 0, 1, 0, 1)}, {f[2](a[1], 1, 0, 0, 1)}] = , [{[%1, %1], [%1, {[a[1]]}]}, {[{[{[%1, %1]}, {[a[1] + 1/2]}]}, {[a[1]]}]}] %1 := {[2 a[1] - 2]} = , [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[1](a[1] - 1, 3, 0, 0, 1), f[1](a[1], 1, 1, 0, 1)}, {f[2](a[1], 2, 0, 0, 1)}] = , [{[{[2 a[1] - 1]}, {[a[1]]}], [2 a[1]]}, {[1 + a[1]]}] = , [{[2 a[1]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, 3 <= a[2], a[3] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 0, 1), f[1](a[1], a[2] - 1, 1, 0, 1)}, {f[2](a[1], a[2], 0, 0, 1)}] = , [{[{[{[2 a[1] + a[2] - 2]}, {[{[2 a[1] + a[2] - 2]}, {[a[1] + 2]}]}]}, {[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}], [{[2 a[1] + a[2] - 3]}, {[a[1]]}]}, {[1 + a[1]]}] = , [{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 2} The value of the game = , [{f[1](0, 1, 1, 0, 1)}, {f[2](0, 2, 0, 0, 1)}] = , [{[0]}, {[{[1/2]}, {[1/2]}]}] = , [1/2] For the domain, {a[5] = 1, 3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[1](0, a[2] - 1, 1, 0, 1)}, {f[2](0, a[2], 0, 0, 1)}] = , [{[{[{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}]}, {[{[-2 + a[2]]}, {[1]}]}]}, {[1]}] = , [{[-2 + a[2]]}, {[1]}] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[1](0, 0, 0, 1, 1)}, {f[2](0, 0, 1, 0, 1)}] = , [{[-2]}, {[-1]}] = , [-3/2] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[1](0, 1, 1, 0, 1), f[1](1, 0, 0, 1, 1)}, {f[2](1, 0, 1, 0, 1)}] = , [{[0]}, {[1]}] = , [1/2] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [ {f[1](a[1], 0, 0, 1, 1), f[1](a[1] - 1, 1, 1, 0, 1)}, {f[2](a[1], 0, 1, 0, 1)}] = , [{[2 a[1] - 2]}, {[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}] = , [{[2 a[1] - 2]}, {[2 a[1] - 2]}] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 2, 1, 0, 1), f[1](a[1], 1, 0, 1, 1), f[1](a[1], 0, 2, 0, 1)}, {f[2](a[1], 1, 1, 0, 1)}] = , [{[{[2 a[1]]}, {[2 a[1]]}], [ {[{[2 a[1] - 1]}, {[{[2 a[1] - 1]}, {[1 + a[1]]}]}]}, {[{[2 a[1] - 1]}, {[a[1]]}]}]}, {[{[2 a[1]]}, {[1 + a[1]]}]}] = , [2 a[1]] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[4] = 0, a[2] = 1} The value of the game = , [ {f[1](0, 1, 0, 1, 1), f[1](0, 0, 2, 0, 1)}, {f[2](0, 1, 1, 0, 1)}] = , [{[{[0]}, {[0]}]}, {[{[0]}, {[1]}]}] = , [0] For the domain, {a[5] = 1, a[3] = 1, 2 <= a[2], a[4] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 1, 0, 1), f[1](a[1], a[2] - 1, 2, 0, 1), f[1](a[1], a[2], 0, 1, 1)}, {f[2](a[1], a[2], 1, 0, 1)}] = , [{[%1, {[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}] , [{[{[2 a[1] + a[2] - 2]}, {[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}]}, {[{[2 a[1] + a[2] - 2]}, {[a[1]]}]}], [ {[{[3 a[1] + 2 a[2] - 2]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, %1 ]}, {[%1, {[1 + a[1]]}]}] %1 := {[2 a[1] + a[2] - 1]} = , [{[{[2 a[1] + a[2] - 1]}, {[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}]}, {[{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}] For the domain, {a[5] = 1, a[3] = 1, 2 <= a[2], a[1] = 0, a[4] = 0} The value of the game = , [ {f[1](0, a[2] - 1, 2, 0, 1), f[1](0, a[2], 0, 1, 1)}, {f[2](0, a[2], 1, 0, 1)}] = , [{[{[a[2] - 1]}, {[{[{[a[2] - 1]}, {[a[2] - 1]}], [{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}, {[{[a[2] - 1]}, {[1]}], [{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}], [ {[{[2 a[2] - 2]}, {[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}]} , {[a[2] - 1]}]}, {[{[a[2] - 1]}, {[1]}]}] = , [{[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}, {[{[a[2] - 1]}, {[1]}]}] For the domain, {a[5] = 1, a[2] = 0, a[4] = 0, 1 <= a[1], a[3] = 2} The value of the game = , [ {f[1](a[1] - 1, 1, 2, 0, 1), f[1](a[1], 0, 1, 1, 1)}, {f[2](a[1], 0, 2, 0, 1)}] = , [{[{[{[3 a[1] - 1]}, {[{[2 a[1] - 1]}, {[{[2 a[1] - 1]}, {[1 + a[1]]}]}]}]}, {[2 a[1] - 1]}], [{[3 a[1]]}, {[{[2 a[1]]}, {[1 + a[1]]}]}]}, {[2 a[1]]}] = , [{[2 a[1]]}, {[2 a[1]]}] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[4] = 0, a[3] = 2} The value of the game = , [{f[1](0, 0, 1, 1, 1)}, {f[2](0, 0, 2, 0, 1)}] = , [{[{[0]}, {[{[0]}, {[0]}]}]}, {[0]}] = , [{[0]}, {[0]}] For the domain, {a[5] = 1, a[4] = 0, 1 <= a[1], a[3] = 2, 1 <= a[2]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 2, 0, 1), f[1](a[1], a[2] - 1, 3, 0, 1), f[1](a[1], a[2], 1, 1, 1)}, {f[2](a[1], a[2], 2, 0, 1)}] = , [{[{[3 a[1] + 2 a[2]]}, {[{[2 a[1] + a[2]]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}], [{[{[3 a[1] - 1 + 2 a[2]]}, {[2 a[1] + a[2] - 1/2]}]}, %1], [ {[{[3 a[1] - 1 + 2 a[2]]}, {[%1, {[%1, {[1 + a[1]]}]}]}]}, %1 ]}, {[2 a[1] + a[2]]}] %1 := {[2 a[1] + a[2] - 1]} = , [{[{[3 a[1] + 2 a[2]]}, {[{[2 a[1] + a[2]]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}]}, {[2 a[1] + a[2]]}] For the domain, {a[5] = 1, a[1] = 0, a[4] = 0, a[3] = 2, 1 <= a[2]} The value of the game = , [ {f[1](0, a[2], 1, 1, 1), f[1](0, a[2] - 1, 3, 0, 1)}, {f[2](0, a[2], 2, 0, 1)}] = , [{[{[2 a[2]]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}], [{[{[2 a[2] - 1]}, {[- 1/2 + a[2]]}]}, {[a[2] - 1]}]}, {[a[2]]}] = , [{[{[2 a[2]]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}]}, {[a[2]]}] For the domain, {a[5] = 1, 3 <= a[3], a[4] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, a[3], 0, 1), f[1](a[1], a[2] - 1, a[3] + 1, 0, 1), f[1](a[1], a[2], a[3] - 1, 1, 1)}, {f[2](a[1], a[2], a[3], 0, 1)}] = , [{[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[2 a[1] + a[2] + 1/2]}], [ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[2 a[1] + a[2] - 1/2]}]}, {[2 a[1] + a[2] - 1]}]}, {[2 a[1] + a[2]]}] = , [{[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[2 a[1] + a[2] + 1/2]}]}, {[2 a[1] + a[2]]}] For the domain, {a[5] = 1, 3 <= a[3], a[2] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{ f[1](a[1] - 1, 1, a[3], 0, 1), f[1](a[1], 0, a[3] - 1, 1, 1)} , {f[2](a[1], 0, a[3], 0, 1)}] = , [{[{[3 a[1] - 2 + a[3]]}, {[2 a[1] + 1/2]}], [{[{[3 a[1] - 3 + a[3]]}, {[2 a[1] - 1/2]}]}, {[2 a[1] - 1]}] }, {[2 a[1]]}] = , [{[{[3 a[1] - 2 + a[3]]}, {[2 a[1] + 1/2]}]}, {[2 a[1]]}] For the domain, {a[5] = 1, 3 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[1](0, a[2] - 1, a[3] + 1, 0, 1), f[1](0, a[2], a[3] - 1, 1, 1)}, {f[2](0, a[2], a[3], 0, 1)}] = , [{[{[-2 + 2 a[2] + a[3]]}, {[1/2 + a[2]]}], [{[{[-3 + 2 a[2] + a[3]]}, {[- 1/2 + a[2]]}]}, {[a[2] - 1]}]} , {[a[2]]}] = , [{[{[-2 + 2 a[2] + a[3]]}, {[1/2 + a[2]]}]}, {[a[2]]}] For the domain, {a[5] = 1, 3 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[1](0, 0, a[3] - 1, 1, 1)}, {f[2](0, 0, a[3], 0, 1)}] = , [{[{[a[3] - 2]}, {[1/2]}]}, {[0]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 1, 0, 1, 1)}, {f[2](a[1], 0, 0, 1, 1)}] = , [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[{[2 a[1] - 2]}, {[a[1]]}]}] = , [2 a[1] - 2] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{}, {f[2](0, 0, 0, 1, 1)}] = , [{}, {[{[-2]}, {[-1]}]}] = , [-2] For the domain, {a[5] = 1, a[4] = 1, a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [ {f[1](a[1] - 1, 2, 0, 1, 1), f[1](a[1], 0, 1, 1, 1)}, {f[2](a[1], 1, 0, 1, 1)}] = , [{[{[3 a[1]]}, {[{[2 a[1]]}, {[1 + a[1]]}]}], [%1, {[ {[%1, %1], [%1, {[%1, {[1 + a[1]]}]}]}, {[%1, {[a[1]]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}]}]}]}, { [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} ] %1 := {[2 a[1] - 1]} = , [{[2 a[1]]}, {[2 a[1]]}] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[3] = 0, a[2] = 1} The value of the game = , [{f[1](0, 0, 1, 1, 1)}, {f[2](0, 1, 0, 1, 1)}] = , [{[{[0]}, {[{[0]}, {[0]}]}]}, {[{[{[0]}, {[0]}]}, {[1/2]}]}] = , [{[0]}, {[0]}] For the domain, {a[5] = 1, a[4] = 1, 2 <= a[2], a[3] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 1, 1), f[1](a[1], a[2] - 1, 1, 1, 1)}, {f[2](a[1], a[2], 0, 1, 1)}] = , [{[%2, {[{[%2, %2], [%2, {[%2, {[1 + a[1]]}]}]}, {[{[%2, {[1 + a[1]]}]}, {[a[1]]}], [%2, {[a[1]]}]}]}], [{[3 a[1] + 2 a[2] - 2]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, {[ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}] %1 := {[2 a[1] + a[2] - 1]} %2 := {[2 a[1] + a[2] - 2]} = , [%1, {[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}] %1 := {[2 a[1] + a[2] - 1]} For the domain, {a[5] = 1, a[4] = 1, 2 <= a[2], a[1] = 0, a[3] = 0} The value of the game = , [{f[1](0, a[2] - 1, 1, 1, 1)}, {f[2](0, a[2], 0, 1, 1)}] = , [{[{[2 a[2] - 2]}, {[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}]} , {[{[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}], [{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[a[2] - 1]}, {[1]}], [{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}] = , [{[a[2] - 1]}, {[{[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}], [{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[a[2] - 1]}, {[1]}], [{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}] For the domain, {a[5] = 1, a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 0} The value of the game = , [{f[1](0, 0, 0, 2, 1)}, {f[2](0, 0, 1, 1, 1)}] = , [{[0]}, {[{[0]}, {[0]}]}] For the domain, {a[5] = 1, a[3] = 1, a[4] = 1, a[2] = 0, 1 <= a[1]} The value of the game = , [ {f[1](a[1] - 1, 1, 1, 1, 1), f[1](a[1], 0, 0, 2, 1)}, {f[2](a[1], 0, 1, 1, 1)}] = , [{[3 a[1]], [{[3 a[1] - 1]}, {[{[2 a[1] - 1]}, {[{[2 a[1] - 1]}, {[1 + a[1]]}]}]}]}, {[{[2 a[1]]}, {[1 + a[1]]}]}] = , [{[3 a[1]]}, {[{[2 a[1]]}, {[1 + a[1]]}]}] For the domain, {a[5] = 1, a[3] = 1, a[4] = 1, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 1, 1, 1), f[1](a[1], a[2] - 1, 2, 1, 1), f[1](a[1], a[2], 0, 2, 1)}, {f[2](a[1], a[2], 1, 1, 1)}] = , [{[3 a[1] + 2 a[2]], [{[3 a[1] - 1 + 2 a[2]]}, {[ {[2 a[1] + a[2] - 1]}, {[{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}]}], [{[3 a[1] - 1 + 2 a[2]]}, {[2 a[1] + a[2] - 1/2]}]}, {[{[2 a[1] + a[2]]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}] = , [{[3 a[1] + 2 a[2]]}, {[{[2 a[1] + a[2]]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}] For the domain, {a[5] = 1, a[3] = 1, a[4] = 1, a[1] = 0, 1 <= a[2]} The value of the game = , [ {f[1](0, a[2] - 1, 2, 1, 1), f[1](0, a[2], 0, 2, 1)}, {f[2](0, a[2], 1, 1, 1)}] = , [{[2 a[2]], [{[2 a[2] - 1]}, {[- 1/2 + a[2]]}]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}] = , [{[2 a[2]]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}] For the domain, {a[5] = 1, a[4] = 1, 2 <= a[3], 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, a[3], 1, 1), f[1](a[1], a[2] - 1, a[3] + 1, 1, 1), f[1](a[1], a[2], a[3] - 1, 2, 1)}, {f[2](a[1], a[2], a[3], 1, 1)}] = , [{[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[2 a[1] + a[2] - 1/2]}], [3 a[1] + 2 a[2] + a[3] - 1]}, {[{[2 a[1] + a[2]]}, {[1 + 2 a[1] + a[2]]}]}] = , [{[3 a[1] + 2 a[2] + a[3] - 1]}, {[2 a[1] + a[2] + 1/2]}] For the domain, {a[5] = 1, a[4] = 1, 2 <= a[3], a[2] = 0, 1 <= a[1]} The value of the game = , [{ f[1](a[1] - 1, 1, a[3], 1, 1), f[1](a[1], 0, a[3] - 1, 2, 1)} , {f[2](a[1], 0, a[3], 1, 1)}] = , [{[{[3 a[1] - 2 + a[3]]}, {[2 a[1] - 1/2]}], [3 a[1] - 1 + a[3]]}, {[{[2 a[1]]}, {[1 + 2 a[1]]}]}] = , [{[3 a[1] - 1 + a[3]]}, {[2 a[1] + 1/2]}] For the domain, {a[5] = 1, a[4] = 1, 2 <= a[3], a[1] = 0, 1 <= a[2]} The value of the game = , [{f[1](0, a[2] - 1, a[3] + 1, 1, 1), f[1](0, a[2], a[3] - 1, 2, 1)}, {f[2](0, a[2], a[3], 1, 1)}] = , [{[2 a[2] + a[3] - 1], [{[-2 + 2 a[2] + a[3]]}, {[- 1/2 + a[2]]}]}, {[{[a[2]]}, {[a[2] + 1]}]}] = , [{[2 a[2] + a[3] - 1]}, {[1/2 + a[2]]}] For the domain, {a[5] = 1, a[4] = 1, 2 <= a[3], a[1] = 0, a[2] = 0} The value of the game = , [{f[1](0, 0, a[3] - 1, 2, 1)}, {f[2](0, 0, a[3], 1, 1)}] = , [{[a[3] - 1]}, {[{[0]}, {[1]}]}] = , [{[a[3] - 1]}, {[1/2]}] For the domain, {a[5] = 1, 2 <= a[4], 1 <= a[1], 1 <= a[2], 1 <= a[3]} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], 1), f[1](a[1], a[2] - 1, a[3] + 1, a[4], 1), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 1)}, {}] = , [{[3 a[1] + 2 a[2] + a[3] - 1]}, {}] = , [3 a[1] + 2 a[2] + a[3]] For the domain, {a[5] = 1, 2 <= a[4], a[3] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, a[4], 1), f[1](a[1], a[2] - 1, 1, a[4], 1)}, {}] = , [{[3 a[1] + 2 a[2] - 1]}, {}] = , [3 a[1] + 2 a[2]] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[1](a[1] - 1, 1, a[3], a[4], 1), f[1](a[1], 0, a[3] - 1, a[4] + 1, 1)}, {}] = , [{[3 a[1] - 1 + a[3]]}, {}] = , [3 a[1] + a[3]] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, a[3] = 0, 1 <= a[1]} The value of the game = , [{f[1](a[1] - 1, 1, 0, a[4], 1)}, {}] = , [{[3 a[1] - 1]}, {}] = , [3 a[1]] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, 1 <= a[2], 1 <= a[3]} The value of the game = , [{f[1](0, a[2] - 1, a[3] + 1, a[4], 1), f[1](0, a[2], a[3] - 1, a[4] + 1, 1)}, {}] = , [{[2 a[2] + a[3] - 1]}, {}] = , [2 a[2] + a[3]] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[3] = 0, 1 <= a[2]} The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], 1)}, {}] = , [{[2 a[2] - 1]}, {}] = , [2 a[2]] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[2] = 0, 1 <= a[3]} The value of the game = , [{f[1](0, 0, a[3] - 1, a[4] + 1, 1)}, {}] = , [{[a[3] - 1]}, {}] = , [a[3]] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{}, {}] = , [{}, {}] = , [0] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{}, {f[2](0, 0, 0, 0, a[5])}] = , [{}, {[-2]}] = , [-3] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [ {f[1](a[1] - 1, 1, 0, 0, a[5])}, {f[2](a[1], 0, 0, 0, a[5])}] = , [{[2 a[1] - 2]}, {[2 a[1] - 2]}] For the domain, {a[3] = 0, a[4] = 0, a[2] = 1, 1 <= a[1], 2 <= a[5]} The value of the game = , [ {f[1](a[1], 0, 1, 0, a[5]), f[1](a[1] - 1, 2, 0, 0, a[5])}, {f[2](a[1], 1, 0, 0, a[5])}] = , [{[2 a[1] - 1]}, {[{[2 a[1]]}, {[2 a[1]]}]}] = , [2 a[1]] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 0, a[5]), f[1](a[1], a[2] - 1, 1, 0, a[5])}, {f[2](a[1], a[2], 0, 0, a[5])}] = , [{[2 a[1] + a[2] - 2], [%1, %1]}, {[%1, %1]}] %1 := {[2 a[1] + a[2] - 1]} = , [2 a[1] + a[2] - 1] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1, 2 <= a[5]} The value of the game = , [{f[1](0, 0, 1, 0, a[5])}, {f[2](0, 1, 0, 0, a[5])}] = , [{[-1]}, {[{[0]}, {[0]}]}] = , [0] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [ {f[1](0, a[2] - 1, 1, 0, a[5])}, {f[2](0, a[2], 0, 0, a[5])}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[a[2] - 1]}, {[a[2] - 1]}]}] = , [a[2] - 1] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [ {f[1](a[1] - 1, 1, 1, 0, a[5]), f[1](a[1], 0, 0, 1, a[5])}, {f[2](a[1], 0, 1, 0, a[5])}] = , [{[{[2 a[1] - 1]}, {[2 a[1] - 1]}]}, {[2 a[1]]}] = , [2 a[1] - 1] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{f[1](0, 0, 0, 1, a[5])}, {f[2](0, 0, 1, 0, a[5])}] = , [{[-2]}, {[0]}] = , [-1] For the domain, {a[3] = 1, a[4] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 1, 0, a[5]), f[1](a[1], a[2] - 1, 2, 0, a[5]), f[1](a[1], a[2], 0, 1, a[5])}, {f[2](a[1], a[2], 1, 0, a[5])} ] = , [{[{[{[3 a[1] + 2 a[2] - 2]}, {[2 a[1] + a[2]]}]}, {[2 a[1] + a[2] - 1]}], [2 a[1] + a[2]], [{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[2 a[1] + a[2]]}] = , [{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, 1 <= a[2], 2 <= a[5]} The value of the game = , [ {f[1](0, a[2] - 1, 2, 0, a[5]), f[1](0, a[2], 0, 1, a[5])}, {f[2](0, a[2], 1, 0, a[5])}] = , [{[a[2]], [{[{[2 a[2] - 2]}, {[a[2]]}]}, {[a[2] - 1]}]}, {[a[2]]}] = , [{[a[2]]}, {[a[2]]}] For the domain, {2 <= a[3], a[4] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], 0, a[5]), f[1](a[1], a[2] - 1, a[3] + 1, 0, a[5]), f[1](a[1], a[2], a[3] - 1, 1, a[5])}, {f[2](a[1], a[2], a[3], 0, a[5])}] = , [{[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[1 + 2 a[1] + a[2]]}], [ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[2 a[1] + a[2]]}]}, {[2 a[1] + a[2] - 1]}]}, {[2 a[1] + a[2]]}] = , [{[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[1 + 2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 1, a[5]), f[1](a[1] - 1, 1, a[3], 0, a[5])}, {f[2](a[1], 0, a[3], 0, a[5])}] = , [{[{[3 a[1] - 2 + a[3]]}, {[1 + 2 a[1]]}], [{[{[3 a[1] - 3 + a[3]]}, {[2 a[1]]}]}, {[2 a[1] - 1]}]}, {[2 a[1]]}] = , [{[{[3 a[1] - 2 + a[3]]}, {[1 + 2 a[1]]}]}, {[2 a[1]]}] For the domain, {2 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[1](0, a[2] - 1, a[3] + 1, 0, a[5]), f[1](0, a[2], a[3] - 1, 1, a[5])}, {f[2](0, a[2], a[3], 0, a[5])}] = , [{[{[-2 + 2 a[2] + a[3]]}, {[a[2] + 1]}], [{[{[-3 + 2 a[2] + a[3]]}, {[a[2]]}]}, {[a[2] - 1]}]}, {[a[2]]}] = , [{[{[-2 + 2 a[2] + a[3]]}, {[a[2] + 1]}]}, {[a[2]]}] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [ {f[1](0, 0, a[3] - 1, 1, a[5])}, {f[2](0, 0, a[3], 0, a[5])}] = , [{[{[a[3] - 2]}, {[1]}]}, {[0]}] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0, 2 <= a[5]} The value of the game = , [{}, {f[2](0, 0, 0, 1, a[5])}] = , [{}, {[-1]}] = , [-2] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [ {f[1](a[1] - 1, 1, 0, 1, a[5])}, {f[2](a[1], 0, 0, 1, a[5])}] = , [{[2 a[1] - 1]}, {[2 a[1] - 1]}] For the domain, {a[4] = 1, a[3] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 1, a[5]), f[1](a[1], a[2] - 1, 1, 1, a[5])}, {f[2](a[1], a[2], 0, 1, a[5])}] = , [{[2 a[1] + a[2] - 1], [{[3 a[1] + 2 a[2] - 2]}, {[2 a[1] + a[2]]}]}, {[{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}]}] = , [2 a[1] + a[2]] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[5]} The value of the game = , [ {f[1](0, a[2] - 1, 1, 1, a[5])}, {f[2](0, a[2], 0, 1, a[5])}] = , [{[{[2 a[2] - 2]}, {[a[2]]}]}, {[{[a[2]]}, {[a[2]]}]}] = , [a[2]] For the domain, {a[4] = 1, 1 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[1](a[1], a[2], a[3] - 1, 2, a[5]), f[1](a[1] - 1, a[2] + 1, a[3], 1, a[5]), f[1](a[1], a[2] - 1, a[3] + 1, 1, a[5])}, {f[2](a[1], a[2], a[3], 1, a[5])}] = , [{[{[3 a[1] + 2 a[2] + a[3] - 2]}, {[2 a[1] + a[2]]}], [3 a[1] + 2 a[2] + a[3] - 1]}, {[1 + 2 a[1] + a[2]]}] = , [{[3 a[1] + 2 a[2] + a[3] - 1]}, {[1 + 2 a[1] + a[2]]}] For the domain, {a[4] = 1, a[2] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 2, a[5]), f[1](a[1] - 1, 1, a[3], 1, a[5])}, {f[2](a[1], 0, a[3], 1, a[5])}] = , [{[3 a[1] - 1 + a[3]], [{[3 a[1] - 2 + a[3]]}, {[2 a[1]]}]}, {[1 + 2 a[1]]}] = , [{[3 a[1] - 1 + a[3]]}, {[1 + 2 a[1]]}] For the domain, {a[4] = 1, a[1] = 0, 1 <= a[2], 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[1](0, a[2], a[3] - 1, 2, a[5]), f[1](0, a[2] - 1, a[3] + 1, 1, a[5])}, {f[2](0, a[2], a[3], 1, a[5])}] = , [{[2 a[2] + a[3] - 1], [{[-2 + 2 a[2] + a[3]]}, {[a[2]]}]}, {[a[2] + 1]}] = , [{[2 a[2] + a[3] - 1]}, {[a[2] + 1]}] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, 2 <= a[5], 1 <= a[3]} The value of the game = , [ {f[1](0, 0, a[3] - 1, 2, a[5])}, {f[2](0, 0, a[3], 1, a[5])}] = , [{[a[3] - 1]}, {[1]}] For the domain, {2 <= a[4], 1 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[3]} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], a[5]), f[1](a[1], a[2], a[3] - 1, a[4] + 1, a[5]), f[1](a[1], a[2] - 1, a[3] + 1, a[4], a[5])}, {}] = , [{[3 a[1] + 2 a[2] + a[3] - 1]}, {}] = , [3 a[1] + 2 a[2] + a[3]] For the domain, {2 <= a[4], a[3] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[1](a[1], a[2] - 1, 1, a[4], a[5]), f[1](a[1] - 1, a[2] + 1, 0, a[4], a[5])}, {}] = , [{[3 a[1] + 2 a[2] - 1]}, {}] = , [3 a[1] + 2 a[2]] For the domain, {2 <= a[4], a[2] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[1](a[1] - 1, 1, a[3], a[4], a[5]), f[1](a[1], 0, a[3] - 1, a[4] + 1, a[5])}, {}] = , [{[3 a[1] - 1 + a[3]]}, {}] = , [3 a[1] + a[3]] For the domain, {2 <= a[4], a[2] = 0, a[3] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [{f[1](a[1] - 1, 1, 0, a[4], a[5])}, {}] = , [{[3 a[1] - 1]}, {}] = , [3 a[1]] For the domain, {2 <= a[4], a[1] = 0, 1 <= a[2], 2 <= a[5], 1 <= a[3]} The value of the game = , [{ f[1](0, a[2], a[3] - 1, a[4] + 1, a[5]), f[1](0, a[2] - 1, a[3] + 1, a[4], a[5])}, {}] = , [{[2 a[2] + a[3] - 1]}, {}] = , [2 a[2] + a[3]] For the domain, {2 <= a[4], a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], a[5])}, {}] = , [{[2 a[2] - 1]}, {}] = , [2 a[2]] For the domain, {2 <= a[4], a[1] = 0, a[2] = 0, 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[1](0, 0, a[3] - 1, a[4] + 1, a[5])}, {}] = , [{[a[3] - 1]}, {}] = , [a[3]] For the domain, {2 <= a[4], a[1] = 0, a[2] = 0, a[3] = 0, 2 <= a[5]} The value of the game = , [{}, {}] = , [{}, {}] = , [0] ########## #, f[2], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{}, {f[3](0, 0, 0, 0, 0), f[5](0, 0, 0, 0) + [0]}] = , [{}, {[-4]}] = , [-5] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, 0, 0, 1)}, {f[3](0, 0, 0, 1, 0), f[5](0, 0, 0, 1) + [0]}] = , [{[-4]}, {[-2]}] = , [-3] For the domain, {2 <= a[4], a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, 0, a[4] - 1, 1)}, {f[5](0, 0, 0, a[4]) + [0], f[3](0, 0, 0, a[4], 0)}] = , [{[{[a[4] - 4]}, {[-1]}]}, {[-2], [{[{[a[4] - 3]}, {[0]}]}, {[-1]}]}] = , [{[{[a[4] - 4]}, {[-1]}]}, {[-2]}] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[2](0, 1, 0, 0, 0)}, {f[5](1, 0, 0, 0) + [0], f[3](1, 0, 0, 0, 0)}] = , [{[{[-2]}, {[-2]}]}, {[-1]}] = , [-2] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [{f[2](a[1] - 1, 1, 0, 0, 0)}, {f[3](a[1], 0, 0, 0, 0), f[5](a[1], 0, 0, 0) + [0]}] = , [{[{[a[1] - 2]}, {[a[1] - 2]}]}, {[{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}]}] = , [a[1] - 2] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[2](0, 0, 1, 0, 0)}, {f[3](0, 1, 0, 0, 0), f[5](0, 1, 0, 0) + [0]}] = , [{[-2]}, {[-2], [{[-1]}, {[-1]}]}] = , [{[-2]}, {[-2]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[2](0, 2, 0, 0, 0), f[2](1, 0, 1, 0, 0)}, {f[5](1, 1, 0, 0) + [0], f[3](1, 1, 0, 0, 0)}] = , [{[0], [{[-1/2]}, {[-1/2]}]}, {[0], [{[1/2]}, {[{[0]}, {[{[0]}, {[3]}]}]}]}] = , [{[0]}, {[0]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[2](a[1] - 1, 2, 0, 0, 0), f[2](a[1], 0, 1, 0, 0)}, {f[3](a[1], 1, 0, 0, 0), f[5](a[1], 1, 0, 0) + [0]}] = , [{[a[1] - 1]}, {[a[1] - 1], [{[a[1] - 1/2]}, {[{[a[1] - 1]}, {[{[a[1] - 1]}, {[3]}]}]}]}] = , [{[a[1] - 1]}, {[a[1] - 1]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 2} The value of the game = , [{f[2](0, 1, 1, 0, 0)}, {f[5](0, 2, 0, 0) + [0], f[3](0, 2, 0, 0, 0)}] = , [{[{[-1]}, {[0]}]}, {[-1/2], [{[1/4]}, {[-1/4]}]}] = , [{[-1/2]}, {[-1/2]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], 4 <= a[2]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 0, 0, 0), f[2](a[1], a[2] - 1, 1, 0, 0)}, {f[5](a[1], a[2], 0, 0) + [0], f[3](a[1], a[2], 0, 0, 0)}] = , [{[{[2 a[1] + a[2] - 5/2]}, {[a[1]]}], [a[1] - 1]}, { [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], [ {[{[2 a[1] + a[2] - 2]}, {[a[1] + 1/2]}]}, {[ {[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}]}]}] = , [a[1]] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], a[2] = 3} The value of the game = , [ {f[2](a[1] - 1, 4, 0, 0, 0), f[2](a[1], 2, 1, 0, 0)}, {f[5](a[1], 3, 0, 0) + [0], f[3](a[1], 3, 0, 0, 0)}] = , [{[a[1] - 1], [{[2 a[1] + 1/2]}, {[a[1]]}]}, { [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], [ {[{[2 a[1] + 1]}, {[a[1] + 1/2]}]}, {[{[{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}]}]}] = , [a[1]] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 3} The value of the game = , [{f[2](0, 2, 1, 0, 0)}, {f[5](0, 3, 0, 0) + [0], f[3](0, 3, 0, 0, 0)}] = , [{[{[1/2]}, {[0]}]}, {[{[1/2]}, {[0]}], [{[{[1]}, {[1/2]}]}, {[{[{[{[0]}, {[1]}]}, {[0]}]}, {[0]}]}]} ] = , [0] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, 4 <= a[2]} The value of the game = , [{f[2](0, a[2] - 1, 1, 0, 0)}, {f[3](0, a[2], 0, 0, 0), f[5](0, a[2], 0, 0) + [0]}] = , [{[{[- 5/2 + a[2]]}, {[0]}]}, {[{[{[1]}, {[1]}]}, {[0]}], [ {[{[-2 + a[2]]}, {[1/2]}]}, {[{[{[{[-3 + a[2]]}, {[1]}]}, {[0]}]}, {[0]}]}]}] = , [0] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[2](a[1], 1, 1, 0, 0), f[2](a[1] - 1, 3, 0, 0, 0)}, {f[5](a[1], 2, 0, 0) + [0], f[3](a[1], 2, 0, 0, 0)}] = , [{[{[2 a[1] - 1]}, {[a[1]]}], [a[1] - 1]}, { [{[a[1]]}, {[a[1]]}], [{[{[2 a[1]]}, {[a[1] + 1/2]}]}, {[{[{[a[1]]}, {[a[1]]}]}, {[a[1]]}]}]}] = , [a[1]] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[1](0, 0, 0, 0, 1)}, {f[3](0, 0, 1, 0, 0), f[5](0, 0, 1, 0) + [0]}] = , [{[-5]}, {[-1]}] = , [-2] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[1](1, 0, 0, 0, 1), f[2](0, 1, 1, 0, 0)}, {f[3](1, 0, 1, 0, 0), f[5](1, 0, 1, 0) + [0]}] = , [{[{[-1]}, {[-1]}], [{[-1]}, {[0]}]}, {[1/2]}] = , [0] For the domain, {a[3] = 1, a[1] = 2, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [ {f[2](1, 1, 1, 0, 0), f[1](2, 0, 0, 0, 1)}, {f[5](2, 0, 1, 0) + [0], f[3](2, 0, 1, 0, 0)}] = , [{[{[1]}, {[1]}]}, {[3/2]}] = , [1] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, 3 <= a[1]} The value of the game = , [ {f[2](a[1] - 1, 1, 1, 0, 0), f[1](a[1], 0, 0, 0, 1)}, {f[5](a[1], 0, 1, 0) + [0], f[3](a[1], 0, 1, 0, 0)}] = , [{[{[{[{[2 a[1] - 4]}, {[2 a[1] - 4]}]}, {[a[1] - 1/2]}]}, {[a[1] - 1]}], [{[2 a[1] - 3]}, {[a[1] - 1]}]}, {[a[1] - 1/2]}] = , [a[1] - 1] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{ f[1](1, 1, 0, 0, 1), f[2](1, 0, 2, 0, 0), f[2](0, 2, 1, 0, 0) }, {f[3](1, 1, 1, 0, 0), f[5](1, 1, 1, 0) + [0]}] = , [{[1], [{[1/2]}, {[0]}]}, {[1], [{[2]}, {[3/2]}]}] = , [{[1]}, {[1]}] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [{f[2](a[1] - 1, 2, 1, 0, 0), f[2](a[1], 0, 2, 0, 0), f[1](a[1], 1, 0, 0, 1)}, {f[3](a[1], 1, 1, 0, 0), f[5](a[1], 1, 1, 0) + [0]}] = , [{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}], [2 a[1] - 1], [{[2 a[1] - 3/2]}, {[a[1] - 1]}]}, {[a[1]], [{[2 a[1]]}, {[a[1] + 1/2]}]}] = , [{[2 a[1] - 1]}, {[a[1]]}] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[2](0, 0, 2, 0, 0), f[1](0, 1, 0, 0, 1)}, {f[5](0, 1, 1, 0) + [0], f[3](0, 1, 1, 0, 0)}] = , [{[-1]}, {[0], [{[0]}, {[1/2]}]}] = , [-1/2] For the domain, {a[3] = 1, 2 <= a[2], a[4] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 1, 0, 0), f[2](a[1], a[2] - 1, 2, 0, 0), f[1](a[1], a[2], 0, 0, 1)}, {f[3](a[1], a[2], 1, 0, 0), f[5](a[1], a[2], 1, 0) + [0]}] = , [{[2 a[1] + a[2] - 3/2], [{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}], [{[2 a[1] + a[2] - 5/2]}, {[a[1] - 1]}]}, {[a[1]], [{[2 a[1] + a[2] - 1]}, {[a[1] + 1/2]}]}] = , [{[2 a[1] + a[2] - 3/2]}, {[a[1]]}] For the domain, {a[3] = 1, 2 <= a[2], a[1] = 0, a[4] = 0, a[5] = 0} The value of the game = , [ {f[2](0, a[2] - 1, 2, 0, 0), f[1](0, a[2], 0, 0, 1)}, {f[5](0, a[2], 1, 0) + [0], f[3](0, a[2], 1, 0, 0)}] = , [{[- 3/2 + a[2]], [{[-2 + a[2]]}, {[1]}]}, {[0], [{[a[2] - 1]}, {[1/2]}]}] = , [{[- 3/2 + a[2]]}, {[0]}] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1, a[3] = 2} The value of the game = , [ {f[2](0, 1, 2, 0, 0), f[1](1, 0, 1, 0, 1)}, {f[5](1, 0, 2, 0) + [0]}] = , [{[1/2]}, {[2]}] = , [1] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, 2 <= a[1], a[3] = 2} The value of the game = , [ {f[2](a[1] - 1, 1, 2, 0, 0), f[1](a[1], 0, 1, 0, 1)}, {f[5](a[1], 0, 2, 0) + [0]}] = , [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}], [2 a[1] - 3/2]}, {[2 a[1]]}] = , [2 a[1] - 1] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 2} The value of the game = , [{f[1](0, 0, 1, 0, 1)}, {f[5](0, 0, 2, 0) + [0]}] = , [{[-3/2]}, {[0]}] = , [-1] For the domain, {a[4] = 0, a[5] = 0, a[2] = 1, 1 <= a[1], a[3] = 2} The value of the game = , [{f[2](a[1] - 1, 2, 2, 0, 0), f[1](a[1], 1, 1, 0, 1), f[2](a[1], 0, 3, 0, 0)}, {f[5](a[1], 1, 2, 0) + [0]}] = , [{[2 a[1] - 1/2], [2 a[1]], [{[{[2 a[1]]}, {[2 a[1]]}]}, {[2 a[1]]}]}, {[2 a[1] + 1]}] = , [2 a[1] + 1/2] For the domain, {2 <= a[2], a[4] = 0, a[5] = 0, 1 <= a[1], a[3] = 2} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 2, 0, 0), f[2](a[1], a[2] - 1, 3, 0, 0), f[1](a[1], a[2], 1, 0, 1)}, {f[5](a[1], a[2], 2, 0) + [0]}] = , [{[2 a[1] + a[2] - 3/2], [{[%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}]}], [{[ {[{[3 a[1] + 2 a[2] - 2]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, %1 ]}, %1]}, {[2 a[1] + a[2]]}] %1 := {[2 a[1] + a[2] - 1]} = , [2 a[1] + a[2] - 1/2] For the domain, {a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 1, a[3] = 2} The value of the game = , [ {f[2](0, 0, 3, 0, 0), f[1](0, 1, 1, 0, 1)}, {f[5](0, 1, 2, 0) + [0]}] = , [{[0], [{[{[0]}, {[0]}]}, {[0]}]}, {[1]}] = , [1/2] For the domain, {2 <= a[2], a[1] = 0, a[4] = 0, a[5] = 0, a[3] = 2} The value of the game = , [ {f[2](0, a[2] - 1, 3, 0, 0), f[1](0, a[2], 1, 0, 1)}, {f[5](0, a[2], 2, 0) + [0]}] = , [{[{[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}, {[{[a[2] - 1]}, {[1]}]}], [{[ {[{[2 a[2] - 2]}, {[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}]} , {[a[2] - 1]}]}, {[a[2] - 1]}]}, {[a[2]]}] = , [- 1/2 + a[2]] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], a[3] = 3} The value of the game = , [ {f[2](a[1] - 1, 1, 3, 0, 0), f[1](a[1], 0, 2, 0, 1)}, {f[5](a[1], 0, 3, 0) + [0]}] = , [{[{[2 a[1]]}, {[2 a[1]]}], [ {[{[{[3 a[1] - 1]}, {[%1, {[%1, {[1 + a[1]]}]}]}]}, %1]}, %1] }, {[2 a[1]]}] %1 := {[2 a[1] - 1]} = , [{[{[2 a[1]]}, {[2 a[1]]}]}, {[2 a[1]]}] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 3} The value of the game = , [{f[1](0, 0, 2, 0, 1)}, {f[5](0, 0, 3, 0) + [0]}] = , [{[{[0]}, {[0]}]}, {[0]}] For the domain, {a[4] = 0, a[5] = 0, 1 <= a[1], 1 <= a[2], a[3] = 3} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 3, 0, 0), f[2](a[1], a[2] - 1, 4, 0, 0), f[1](a[1], a[2], 2, 0, 1)}, {f[5](a[1], a[2], 3, 0) + [0]}] = , [{[ {[{[{[3 a[1] - 1 + 2 a[2]]}, {[2 a[1] + a[2] - 1/2]}]}, %2]}, %2], [{[ {[{[3 a[1] - 1 + 2 a[2]]}, {[%2, {[%2, {[1 + a[1]]}]}]}]}, %2 ]}, %2], [{[{[3 a[1] + 2 a[2]]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, %1]}, %1] %1 := {[2 a[1] + a[2]]} %2 := {[2 a[1] + a[2] - 1]} = , [{[{[{[3 a[1] + 2 a[2]]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, %1]} , %1] %1 := {[2 a[1] + a[2]]} For the domain, {a[1] = 0, a[4] = 0, a[5] = 0, 1 <= a[2], a[3] = 3} The value of the game = , [ {f[2](0, a[2] - 1, 4, 0, 0), f[1](0, a[2], 2, 0, 1)}, {f[5](0, a[2], 3, 0) + [0]}] = , [{ [{[{[2 a[2]]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}]}, {[a[2]]}] , [{[{[{[2 a[2] - 1]}, {[- 1/2 + a[2]]}]}, {[a[2] - 1]}]}, {[a[2] - 1]}]}, {[a[2]]}] = , [{ [{[{[2 a[2]]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}]}, {[a[2]]}] }, {[a[2]]}] For the domain, {a[4] = 0, a[5] = 0, 1 <= a[1], 1 <= a[2], 4 <= a[3]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, a[3], 0, 0), f[2](a[1], a[2] - 1, a[3] + 1, 0, 0), f[1](a[1], a[2], a[3] - 1, 0, 1)}, {f[5](a[1], a[2], a[3], 0) + [0]}] = , [{[ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[2 a[1] + a[2] + 1/2]}]}, {[2 a[1] + a[2]]}], [{[ {[{[3 a[1] - 4 + 2 a[2] + a[3]]}, {[2 a[1] + a[2] - 1/2]}]}, {[2 a[1] + a[2] - 1]}]}, {[2 a[1] + a[2] - 1]}]}, {[2 a[1] + a[2]]}] = , [{[ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[2 a[1] + a[2] + 1/2]}]}, {[2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], 4 <= a[3]} The value of the game = , [{ f[2](a[1] - 1, 1, a[3], 0, 0), f[1](a[1], 0, a[3] - 1, 0, 1)} , {f[5](a[1], 0, a[3], 0) + [0]}] = , [{[{[{[3 a[1] - 3 + a[3]]}, {[2 a[1] + 1/2]}]}, {[2 a[1]]}], [ { [{[{[3 a[1] - 4 + a[3]]}, {[2 a[1] - 1/2]}]}, {[2 a[1] - 1]}] }, {[2 a[1] - 1]}]}, {[2 a[1]]}] = , [{[{[{[3 a[1] - 3 + a[3]]}, {[2 a[1] + 1/2]}]}, {[2 a[1]]}]}, {[2 a[1]]}] For the domain, {a[1] = 0, a[4] = 0, a[5] = 0, 1 <= a[2], 4 <= a[3]} The value of the game = , [{f[2](0, a[2] - 1, a[3] + 1, 0, 0), f[1](0, a[2], a[3] - 1, 0, 1)}, {f[5](0, a[2], a[3], 0) + [0]}] = , [{[{[{[-3 + 2 a[2] + a[3]]}, {[1/2 + a[2]]}]}, {[a[2]]}], [{ [{[{[-4 + 2 a[2] + a[3]]}, {[- 1/2 + a[2]]}]}, {[a[2] - 1]}]} , {[a[2] - 1]}]}, {[a[2]]}] = , [{[{[{[-3 + 2 a[2] + a[3]]}, {[1/2 + a[2]]}]}, {[a[2]]}]}, {[a[2]]}] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, 4 <= a[3]} The value of the game = , [{f[1](0, 0, a[3] - 1, 0, 1)}, {f[5](0, 0, a[3], 0) + [0]}] = , [{[{[{[a[3] - 3]}, {[1/2]}]}, {[0]}]}, {[0]}] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[2](0, 1, 0, 1, 0), f[2](1, 0, 0, 0, 1)}, {f[5](1, 0, 0, 1) + [0], f[3](1, 0, 0, 1, 0)}] = , [{[-1]}, {[0], [{[0]}, {[0]}]}] = , [-1/2] For the domain, {a[4] = 1, a[1] = 2, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [ {f[2](2, 0, 0, 0, 1), f[2](1, 1, 0, 1, 0)}, {f[3](2, 0, 0, 1, 0), f[5](2, 0, 0, 1) + [0]}] = , [{[1]}, {[1], [{[3/2]}, {[3/2]}]}] = , [{[1]}, {[1]}] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 3} The value of the game = , [ {f[2](3, 0, 0, 0, 1), f[2](2, 1, 0, 1, 0)}, {f[5](3, 0, 0, 1) + [0], f[3](3, 0, 0, 1, 0)}] = , [{[2]}, {[2], [{[5/2]}, {[5/2]}]}] = , [{[2]}, {[2]}] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 4} The value of the game = , [ {f[2](4, 0, 0, 0, 1), f[2](3, 1, 0, 1, 0)}, {f[5](4, 0, 0, 1) + [0], f[3](4, 0, 0, 1, 0)}] = , [{[3]}, {[3], [27/8]}] = , [{[3]}, {[3]}] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, 5 <= a[1]} The value of the game = , [ {f[2](a[1], 0, 0, 0, 1), f[2](a[1] - 1, 1, 0, 1, 0)}, {f[3](a[1], 0, 0, 1, 0), f[5](a[1], 0, 0, 1) + [0]}] = , [{[a[1] - 1]}, {[a[1] - 1], [{[a[1] - 1]}, {[{[a[1] - 1]}, {[5]}]}]}] = , [{[a[1] - 1]}, {[a[1] - 1]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1, a[4] = 2} The value of the game = , [ {f[2](0, 1, 0, 2, 0), f[2](1, 0, 0, 1, 1)}, {f[5](1, 0, 0, 2) + [0], f[3](1, 0, 0, 2, 0)}] = , [{[{[{[{[0]}, {[0]}]}, {[1/2]}]}, {[-1/2]}], [{[0]}, {[1]}]}, {[0], [{[5/4]}, {[1/2]}]}] = , [{[1/2]}, {[0]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1, 3 <= a[4]} The value of the game = , [ {f[2](1, 0, 0, a[4] - 1, 1), f[2](0, 1, 0, a[4], 0)}, {f[3](1, 0, 0, a[4], 0), f[5](1, 0, 0, a[4]) + [0]}] = , [{[{[{[{[-2 + a[4]]}, {[-2 + a[4]]}]}, {[1/2]}]}, {[-1/2]}], [{[-2 + a[4]]}, {[1]}]}, {[0], [{[{[a[4] - 1]}, {[3/2]}]}, {[1/2]}]}] = , [{[{[-2 + a[4]]}, {[1]}]}, {[0]}] For the domain, {a[1] = 2, a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2} The value of the game = , [ {f[2](2, 0, 0, 1, 1), f[2](1, 1, 0, 2, 0)}, {f[5](2, 0, 0, 2) + [0], f[3](2, 0, 0, 2, 0)}] = , [{[{[2]}, {[2]}], [{[{[{[2]}, {[2]}]}, {[{[2]}, {[2]}]}]}, {[{[1]}, {[1]}]}]}, {[1], [{[{[3]}, {[5/2]}]}, {[3/2]}]}] = , [{[{[2]}, {[2]}]}, {[1]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 3} The value of the game = , [ {f[2](3, 0, 0, 1, 1), f[2](2, 1, 0, 2, 0)}, {f[3](3, 0, 0, 2, 0), f[5](3, 0, 0, 2) + [0]}] = , [{[{[4]}, {[3]}], [{[{[{[4]}, {[4]}]}, {[{[3]}, {[3]}]}]}, {[{[2]}, {[2]}]}]}, {[2], [{[{[5]}, {[7/2]}]}, {[5/2]}]}] = , [{[{[4]}, {[3]}]}, {[2]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 4} The value of the game = , [ {f[2](4, 0, 0, 1, 1), f[2](3, 1, 0, 2, 0)}, {f[3](4, 0, 0, 2, 0), f[5](4, 0, 0, 2) + [0]}] = , [{[{[6]}, {[4]}], [{[{[{[6]}, {[6]}]}, {[{[4]}, {[4]}]}]}, {[{[3]}, {[3]}]}]}, {[3], [{[{[7]}, {[9/2]}]}, {[7/2]}]}] = , [{[{[6]}, {[4]}]}, {[3]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 5} The value of the game = , [ {f[2](5, 0, 0, 1, 1), f[2](4, 1, 0, 2, 0)}, {f[5](5, 0, 0, 2) + [0], f[3](5, 0, 0, 2, 0)}] = , [{[{[{[{[8]}, {[8]}]}, {[{[5]}, {[5]}]}]}, {[{[4]}, {[4]}]}], [{[8]}, {[5]}]}, {[{[{[9]}, {[11/2]}]}, {[9/2]}], [4]}] = , [{[{[8]}, {[5]}]}, {[4]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 6} The value of the game = , [ {f[2](6, 0, 0, 1, 1), f[2](5, 1, 0, 2, 0)}, {f[5](6, 0, 0, 2) + [0], f[3](6, 0, 0, 2, 0)}] = , [{ [{[{[{[10]}, {[10]}]}, {[{[6]}, {[6]}]}]}, {[{[5]}, {[5]}]}], [{[10]}, {[6]}]}, {[5], [{[{[11]}, {[{[6]}, {[6]}]}]}, {[11/2]}]}] = , [{[{[10]}, {[6]}]}, {[5]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, 7 <= a[1]} The value of the game = , [ {f[2](a[1], 0, 0, 1, 1), f[2](a[1] - 1, 1, 0, 2, 0)}, {f[3](a[1], 0, 0, 2, 0), f[5](a[1], 0, 0, 2) + [0]}] = , [{[{ [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[{[a[1]]}, {[a[1]]}]}]} , {[{[a[1] - 1]}, {[a[1] - 1]}]}], [{[2 a[1] - 2]}, {[a[1]]}] }, {[a[1] - 1], [{[a[1]]}, {[a[1] - 1/2]}]}] = , [{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, 2 <= a[1], 3 <= a[4]} The value of the game = , [{ f[2](a[1], 0, 0, a[4] - 1, 1), f[2](a[1] - 1, 1, 0, a[4], 0)} , {f[3](a[1], 0, 0, a[4], 0), f[5](a[1], 0, 0, a[4]) + [0]}] = , [{[{[2 a[1] + a[4] - 4]}, {[a[1]]}], [{[ {[{[2 a[1] + a[4] - 4]}, {[2 a[1] + a[4] - 4]}]}, {[{[a[1]]}, {[a[1]]}]}]}, {[{[a[1] - 1]}, {[a[1] - 1]}]}]}, { [a[1] - 1], [{[{[2 a[1] + a[4] - 3]}, {[a[1] + 1/2]}]}, {[a[1] - 1/2]}]}] = , [{[{[2 a[1] + a[4] - 4]}, {[a[1]]}]}, {[a[1] - 1]}] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[2](0, 0, 1, 1, 0), f[2](0, 1, 0, 0, 1)}, {f[5](0, 1, 0, 1) + [0], f[3](0, 1, 0, 1, 0)}] = , [{[{[-1]}, {[-1]}]}, {[-1/2]}] = , [-1] For the domain, {2 <= a[4], a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[2](0, 1, 0, a[4] - 1, 1), f[2](0, 0, 1, a[4], 0)}, {f[3](0, 1, 0, a[4], 0), f[5](0, 1, 0, a[4]) + [0]}] = , [{[{[{[-2 + a[4]]}, {[-2 + a[4]]}]}, {[1/2]}], [{[{[-2 + a[4]]}, {[0]}]}, {[-1]}]}, {[-1/2], [{[{[-2 + a[4]]}, {[1]}]}, {[0]}]}] = , [{[{[{[-2 + a[4]]}, {[-2 + a[4]]}]}, {[1/2]}]}, {[-1/2]}] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{ f[2](1, 0, 1, 1, 0), f[2](1, 1, 0, 0, 1), f[2](0, 2, 0, 1, 0) }, {f[5](1, 1, 0, 1) + [0], f[3](1, 1, 0, 1, 0)}] = , [{[1/2], [{[1]}, {[1]}]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [{f[2](a[1], 0, 1, 1, 0), f[2](a[1] - 1, 2, 0, 1, 0), f[2](a[1], 1, 0, 0, 1)}, {f[3](a[1], 1, 0, 1, 0), f[5](a[1], 1, 0, 1) + [0]}] = , [{[{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}], [{[a[1]]}, {[a[1]]}]}, {[{[a[1]]}, {[a[1]]}]}] = , [a[1]] For the domain, {a[3] = 0, a[5] = 0, a[2] = 1, 1 <= a[1], a[4] = 2} The value of the game = , [{f[2](a[1] - 1, 2, 0, 2, 0), f[2](a[1], 1, 0, 1, 1), f[2](a[1], 0, 1, 2, 0)}, {f[3](a[1], 1, 0, 2, 0), f[5](a[1], 1, 0, 2) + [0]}] = , [{[{[{[%1, {[%1, {[1 + a[1]]}]}], [%1, %1]}, {[{[%1, {[1 + a[1]]}]}, {[a[1]]}], [%1, {[a[1]]}]}]}, {[{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}], [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, { [{[a[1]]}, {[a[1]]}], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}] %1 := {[2 a[1] - 1]} = , [{[{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] }, {[{[a[1]]}, {[a[1]]}]}] For the domain, {a[3] = 0, a[5] = 0, a[2] = 1, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[2](a[1] - 1, 2, 0, a[4], 0), f[2](a[1], 1, 0, a[4] - 1, 1), f[2](a[1], 0, 1, a[4], 0)}, {f[5](a[1], 1, 0, a[4]) + [0], f[3](a[1], 1, 0, a[4], 0)}] = , [{[{[%1, %1]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}], [{[ {[{[2 a[1] + a[4] - 3]}, {[2 a[1] + a[4] - 3]}]}, {[{[{[2 a[1] - 1]}, {[1 + a[1]]}]}, {[a[1]]}]}]}, {[{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}]}, {[{[a[1]]}, {[a[1]]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}]}] %1 := {[2 a[1] + a[4] - 2]} = , [{[{[{[2 a[1] + a[4] - 2]}, {[2 a[1] + a[4] - 2]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}, {[{[a[1]]}, {[a[1]]}]}] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 2} The value of the game = , [ {f[2](0, 2, 0, 0, 1), f[2](0, 1, 1, 1, 0)}, {f[3](0, 2, 0, 1, 0), f[5](0, 2, 0, 1) + [0]}] = , [{[{[1/2]}, {[1/2]}]}, {[{[1/2]}, {[0]}], [{[{[0]}, {[1]}]}, {[0]}]}] = , [1/2] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [{f[2](a[1] - 1, 3, 0, 1, 0), f[2](a[1], 1, 1, 1, 0), f[2](a[1], 2, 0, 0, 1)}, {f[3](a[1], 2, 0, 1, 0), f[5](a[1], 2, 0, 1) + [0]}] = , [{[1 + a[1]], [{[a[1]]}, {[a[1]]}], [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} , {[{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}] = , [{[1 + a[1]]}, {[1 + a[1]]}] For the domain, {a[4] = 1, 3 <= a[2], a[3] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 0, 1, 0), f[2](a[1], a[2] - 1, 1, 1, 0), f[2](a[1], a[2], 0, 0, 1)}, {f[3](a[1], a[2], 0, 1, 0), f[5](a[1], a[2], 0, 1) + [0]}] = , [{[1 + a[1]], [{[%1, %1]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], [{[a[1]]}, {[a[1]]}]}, {[{[%1, {[1 + a[1]]}]}, {[a[1]]}], [{[ {[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}]}, {[a[1]]}]}] %1 := {[2 a[1] + a[2] - 2]} = , [{[1 + a[1]]}, {[1 + a[1]]}] For the domain, {a[4] = 1, 3 <= a[2], a[1] = 0, a[3] = 0, a[5] = 0} The value of the game = , [ {f[2](0, a[2] - 1, 1, 1, 0), f[2](0, a[2], 0, 0, 1)}, {f[3](0, a[2], 0, 1, 0), f[5](0, a[2], 0, 1) + [0]}] = , [{[{[{[-2 + a[2]]}, {[-2 + a[2]]}]}, {[{[1]}, {[1]}]}], [1]}, {[{[{[{[{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}], [{[-2 + a[2]]}, {[-2 + a[2]]}]}, {[{[-2 + a[2]]}, {[1]}], [{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]} , {[1]}]}, {[0]}], [{[{[-2 + a[2]]}, {[1]}]}, {[0]}]}] = , [{[1]}, {[1]}] For the domain, {2 <= a[2], a[3] = 0, a[5] = 0, 1 <= a[1], a[4] = 2} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 0, 2, 0), f[2](a[1], a[2] - 1, 1, 2, 0), f[2](a[1], a[2], 0, 1, 1)}, {f[3](a[1], a[2], 0, 2, 0), f[5](a[1], a[2], 0, 2) + [0]}] = , [{[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}], [{[%1, {[%1, {[a[1] + 2]}]}]}, {%3, [a[1] + 2]}], [{ [{[%2, %2], [%2, {%3}]}, {[{%3}, {[a[1]]}], [%2, {[a[1]]}]}]} , {[{[{[2 a[1] + a[2] - 3]}, {[a[1]]}]}, {[a[1] - 1]}]}]}, {[{%3}, {[a[1]]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}]}] %1 := {[2 a[1] + a[2] - 1]} %2 := {[2 a[1] + a[2] - 2]} %3 := [%2, {[1 + a[1]]}] = , [{[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}] %1 := {[2 a[1] + a[2] - 1]} For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, a[5] = 0, a[4] = 2} The value of the game = , [ {f[2](0, a[2] - 1, 1, 2, 0), f[2](0, a[2], 0, 1, 1)}, {f[3](0, a[2], 0, 2, 0), f[5](0, a[2], 0, 2) + [0]}] = , [{[{[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}], [{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[a[2] - 1]}, {[1]}], [{[{[a[2] - 1]}, {[2]}]}, {[1]}]}], [ {[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}, {[2], [{[-2 + a[2]]}, {[1]}]}]}, { [{[{[-2 + a[2]]}, {[1]}]}, {[0]}], [{[{[a[2] - 1]}, {[1]}]}, {[0]}]}] = , [{[{[{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}], [{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[a[2] - 1]}, {[1]}], [{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}, {[{[{[-2 + a[2]]}, {[1]}]}, {[0]}]}] For the domain, {2 <= a[2], a[3] = 0, a[5] = 0, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[2](a[1], a[2] - 1, 1, a[4], 0), f[2](a[1], a[2], 0, a[4] - 1, 1), f[2](a[1] - 1, a[2] + 1, 0, a[4], 0)}, { f[3](a[1], a[2], 0, a[4], 0), f[5](a[1], a[2], 0, a[4]) + [0] }] = , [{[{[{ [{[2 a[1] - 4 + a[2] + a[4]]}, {[2 a[1] - 4 + a[2] + a[4]]}]} , {[{%2}, {[a[1]]}]}]}, {[{[{[2 a[1] + a[2] - 3]}, {[a[1]]}]}, {[a[1] - 1]}]}], [ {[%1, %1]}, {[{[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}], [ {[%1, {[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}]}, {%2, [a[1] + 2]}]}, {[{%2}, {[a[1]]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}]}] %1 := {[2 a[1] + a[2] + a[4] - 3]} %2 := [{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}] = , [{[{ [{[2 a[1] + a[2] + a[4] - 3]}, {[2 a[1] + a[2] + a[4] - 3]}]} , {[{[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}]} , {[{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, a[5] = 0, 3 <= a[4]} The value of the game = , [{ f[2](0, a[2], 0, a[4] - 1, 1), f[2](0, a[2] - 1, 1, a[4], 0)} , {f[5](0, a[2], 0, a[4]) + [0], f[3](0, a[2], 0, a[4], 0)}] = , [{[{[%1, {[{[a[2] - 1]}, {[2]}]}]}, {[2], [{[-2 + a[2]]}, {[1]}]}], [{[%1, %1]}, {[{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}, {[{[{[-2 + a[2]]}, {[1]}]}, {[0]}], [{[%1, {[1]}]}, {[0]}]}] %1 := {[-3 + a[2] + a[4]]} = , [{[{[{[-3 + a[2] + a[4]]}, {[-3 + a[2] + a[4]]}]}, {[{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}, {[{[{[-2 + a[2]]}, {[1]}]}, {[0]}]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, 1, 0, 1)}, {f[3](0, 0, 1, 1, 0), f[5](0, 0, 1, 1) + [0]}] = , [{[-1]}, {[-1], [{[0]}, {[0]}]}] = , [{[-1]}, {[-1]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[2](0, 1, 1, 1, 0), f[2](1, 0, 1, 0, 1)}, {f[5](1, 0, 1, 1) + [0], f[3](1, 0, 1, 1, 0)}] = , [{[1], [{[1/2]}, {[1/2]}]}, {[1], [{[3/2]}, {[3/2]}]}] = , [{[1]}, {[1]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [ {f[2](a[1] - 1, 1, 1, 1, 0), f[2](a[1], 0, 1, 0, 1)}, {f[5](a[1], 0, 1, 1) + [0], f[3](a[1], 0, 1, 1, 0)}] = , [{[{[%1, %1]}, {[a[1] + 1/2]}], [{[%1, %1]}, {[{[a[1]]}, {[a[1]]}]}]}, {[a[1]], [{[a[1] + 1/2]}, {[a[1] + 1/2]}]}] %1 := {[2 a[1] - 2]} = , [{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[2](0, 0, 2, 1, 0), f[2](0, 1, 1, 0, 1)}, {f[3](0, 1, 1, 1, 0), f[5](0, 1, 1, 1) + [0]}] = , [{[{[0]}, {[0]}], [{[0]}, {[1]}]}, {[{[1]}, {[1]}], [{[0]}, {[1]}]}] = , [{[1/2]}, {[1/2]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, 2, 1, 1, 0), f[2](a[1], 0, 2, 1, 0), f[2](a[1], 1, 1, 0, 1)}, {f[3](a[1], 1, 1, 1, 0), f[5](a[1], 1, 1, 1) + [0]}] = , [{[{[2 a[1]]}, {[2 a[1]]}], [{[2 a[1]]}, {[1 + a[1]]}], [{[{[2 a[1] - 1]}, {[2 a[1] - 1]}]}, {[{[a[1]]}, {[a[1]]}]}]} , {[{[1 + a[1]]}, {[1 + a[1]]}], [{[2 a[1]]}, {[1 + a[1]]}]}] = , [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] For the domain, {a[3] = 1, a[4] = 1, 2 <= a[2], a[5] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 1, 1, 0), f[2](a[1], a[2] - 1, 2, 1, 0), f[2](a[1], a[2], 1, 0, 1)}, {f[3](a[1], a[2], 1, 1, 0), f[5](a[1], a[2], 1, 1) + [0]}] = , [{[%1, %1], [%1, {[1 + a[1]]}], [ {[{[2 a[1] + a[2] - 2]}, {[2 a[1] + a[2] - 2]}]}, {[{[a[1]]}, {[a[1]]}]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}], [%1, {[1 + a[1]]}]}] %1 := {[2 a[1] + a[2] - 1]} = , [{[{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] For the domain, {a[3] = 1, a[4] = 1, 2 <= a[2], a[1] = 0, a[5] = 0} The value of the game = , [ {f[2](0, a[2] - 1, 2, 1, 0), f[2](0, a[2], 1, 0, 1)}, {f[3](0, a[2], 1, 1, 0), f[5](0, a[2], 1, 1) + [0]}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}], [{[a[2] - 1]}, {[1]}]}, {[{[1]}, {[1]}], [{[a[2] - 1]}, {[1]}]}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[1]}, {[1]}]}] For the domain, {2 <= a[4], a[3] = 1, a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, 1, a[4] - 1, 1)}, {f[3](0, 0, 1, a[4], 0), f[5](0, 0, 1, a[4]) + [0]}] = , [{[{[-2 + a[4]]}, {[0]}]}, {[-1], [{[{[a[4] - 1]}, {[1]}]}, {[0]}]}] = , [{[{[-2 + a[4]]}, {[0]}]}, {[-1]}] For the domain, {a[3] = 1, a[2] = 0, a[5] = 0, 1 <= a[1], a[4] = 2} The value of the game = , [ {f[2](a[1] - 1, 1, 1, 2, 0), f[2](a[1], 0, 1, 1, 1)}, {f[5](a[1], 0, 1, 2) + [0], f[3](a[1], 0, 1, 2, 0)}] = , [{[{[2 a[1]]}, {[1 + a[1]]}], [ {[{[2 a[1] - 1]}, {[{[2 a[1] - 1]}, {[1 + a[1]]}]}]}, {[1 + a[1]], [{[2 a[1] - 2]}, {[a[1]]}]}]}, { [a[1]], [{[{[2 a[1] + 1]}, {[a[1] + 3/2]}]}, {[a[1] + 1/2]}]} ] = , [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[3] = 1, a[2] = 0, a[5] = 0, 1 <= a[1], 3 <= a[4]} The value of the game = , [{ f[2](a[1] - 1, 1, 1, a[4], 0), f[2](a[1], 0, 1, a[4] - 1, 1)} , {f[3](a[1], 0, 1, a[4], 0), f[5](a[1], 0, 1, a[4]) + [0]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}], [ {[{[2 a[1] + a[4] - 3]}, {[{[2 a[1] - 1]}, {[1 + a[1]]}]}]}, {[1 + a[1]], [{[2 a[1] - 2]}, {[a[1]]}]}]}, {[a[1]], [{[{[2 a[1] - 1 + a[4]]}, {[a[1] + 3/2]}]}, {[a[1] + 1/2]}]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {2 <= a[4], a[3] = 1, a[5] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 1, a[4], 0), f[2](a[1], a[2] - 1, 2, a[4], 0), f[2](a[1], a[2], 1, a[4] - 1, 1)}, { f[5](a[1], a[2], 1, a[4]) + [0], f[3](a[1], a[2], 1, a[4], 0) }] = , [{[{[2 a[1] + a[2] + a[4] - 2]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}], [ {[{[2 a[1] + a[2] + a[4] - 3]}, {[2 a[1] + a[2]]}]}, {[2 a[1] + a[2] - 1]}], [{[{[2 a[1] + a[2] + a[4] - 3]}, {[{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}]}, {[1 + a[1]], [{[2 a[1] + a[2] - 2]}, {[a[1]]}]}]}, { [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}], [ {[{[a[4] + 2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}] }] = , [{[{[2 a[1] + a[2] + a[4] - 2]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}, {[a[1] + 2], [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}] For the domain, {2 <= a[4], a[3] = 1, a[1] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{ f[2](0, a[2] - 1, 2, a[4], 0), f[2](0, a[2], 1, a[4] - 1, 1)} , {f[3](0, a[2], 1, a[4], 0), f[5](0, a[2], 1, a[4]) + [0]}] = , [{[{[-2 + a[2] + a[4]]}, {[{[a[2]]}, {[2]}]}], [{[{[-3 + a[2] + a[4]]}, {[a[2]]}]}, {[a[2] - 1]}]}, { [{[{[a[4] - 1 + a[2]]}, {[2]}]}, {[1]}], [{[a[2] - 1]}, {[1]}]}] = , [{[{[-2 + a[2] + a[4]]}, {[{[a[2]]}, {[2]}]}]}, {[2], [{[a[2] - 1]}, {[1]}]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, a[3], 1, 0), f[2](a[1], a[2] - 1, a[3] + 1, 1, 0), f[2](a[1], a[2], a[3], 0, 1)}, {f[5](a[1], a[2], a[3], 1) + [0]}] = , [{[2 a[1] + a[2]], [{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[2 a[1] + a[2]]}] = , [{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [ {f[2](a[1], 0, a[3], 0, 1), f[2](a[1] - 1, 1, a[3], 1, 0)}, {f[5](a[1], 0, a[3], 1) + [0]}] = , [{[2 a[1]], [{[2 a[1] - 1]}, {[2 a[1] - 1]}]}, {[2 a[1]]}] = , [{[2 a[1]]}, {[2 a[1]]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{ f[2](0, a[2] - 1, a[3] + 1, 1, 0), f[2](0, a[2], a[3], 0, 1)} , {f[5](0, a[2], a[3], 1) + [0]}] = , [{[a[2]], [{[a[2] - 1]}, {[a[2] - 1]}]}, {[a[2]]}] = , [{[a[2]]}, {[a[2]]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, a[3], 0, 1)}, {f[5](0, 0, a[3], 1) + [0]}] = , [{[0]}, {[0]}] For the domain, {2 <= a[4], 2 <= a[3], a[5] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{ f[2](a[1], a[2] - 1, a[3] + 1, a[4], 0), f[2](a[1] - 1, a[2] + 1, a[3], a[4], 0), f[2](a[1], a[2], a[3], a[4] - 1, 1)}, {f[5](a[1], a[2], a[3], a[4]) + [0]}] = , [{[{[2 a[1] + a[2] + a[4] - 2]}, {[1 + 2 a[1] + a[2]]}], [ {[{[2 a[1] + a[2] + a[4] - 3]}, {[2 a[1] + a[2]]}]}, {[2 a[1] + a[2] - 1]}]}, {[2 a[1] + a[2]]}] = , [{[{[2 a[1] + a[2] + a[4] - 2]}, {[1 + 2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}] For the domain, {2 <= a[4], 2 <= a[3], a[2] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, 1, a[3], a[4], 0), f[2](a[1], 0, a[3], a[4] - 1, 1)}, {f[5](a[1], 0, a[3], a[4]) + [0]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + 2 a[1]]}], [{[{[2 a[1] + a[4] - 3]}, {[2 a[1]]}]}, {[2 a[1] - 1]}]}, {[2 a[1]]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + 2 a[1]]}]}, {[2 a[1]]}] For the domain, {2 <= a[4], 2 <= a[3], a[1] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[2](0, a[2] - 1, a[3] + 1, a[4], 0), f[2](0, a[2], a[3], a[4] - 1, 1)}, {f[5](0, a[2], a[3], a[4]) + [0]}] = , [{[{[-2 + a[2] + a[4]]}, {[a[2] + 1]}], [{[{[-3 + a[2] + a[4]]}, {[a[2]]}]}, {[a[2] - 1]}]}, {[a[2]]} ] = , [{[{[-2 + a[2] + a[4]]}, {[a[2] + 1]}]}, {[a[2]]}] For the domain, {2 <= a[4], 2 <= a[3], a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, a[3], a[4] - 1, 1)}, {f[5](0, 0, a[3], a[4]) + [0]}] = , [{[{[-2 + a[4]]}, {[1]}]}, {[0]}] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{}, {f[5](0, 0, 0, 0) + [1], f[3](0, 0, 0, 0, 1)}] = , [{}, {[-3]}] = , [-4] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[3] = 0, 1 <= a[4]} The value of the game = , [{f[2](0, 0, 0, a[4] - 1, 2)}, {f[5](0, 0, 0, a[4]) + [1], f[3](0, 0, 0, a[4], 1)}] = , [{[a[4] - 3]}, {[-1], [{[-2 + a[4]]}, {[0]}]}] = , [{[a[4] - 3]}, {[-1]}] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[2](0, 1, 0, 0, 1)}, {f[5](1, 0, 0, 0) + [1], f[3](1, 0, 0, 0, 1)}] = , [{[{[-1]}, {[-1]}]}, {[0]}] = , [-1] For the domain, {a[5] = 1, a[1] = 2, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[2](1, 1, 0, 0, 1)}, {f[5](2, 0, 0, 0) + [1], f[3](2, 0, 0, 0, 1)}] = , [{[{[1]}, {[1]}]}, {[{[1]}, {[{[1]}, {[4]}]}]}] = , [1] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, 3 <= a[1]} The value of the game = , [{f[2](a[1] - 1, 1, 0, 0, 1)}, {f[5](a[1], 0, 0, 0) + [1], f[3](a[1], 0, 0, 0, 1)}] = , [{[{[{[{[2 a[1] - 4]}, {[2 a[1] - 4]}]}, {[a[1] - 1/2]}]}, {[a[1] - 1]}]}, {[{[a[1] - 1]}, {[{[a[1] - 1]}, {[4]}]}]}] = , [a[1] - 1] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[2](0, 0, 1, 0, 1)}, {f[3](0, 1, 0, 0, 1), f[5](0, 1, 0, 0) + [1]}] = , [{[-1]}, {[-1], [{[0]}, {[0]}]}] = , [{[-1]}, {[-1]}] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[2](1, 0, 1, 0, 1), f[2](0, 2, 0, 0, 1)}, {f[5](1, 1, 0, 0) + [1], f[3](1, 1, 0, 0, 1)}] = , [{[1], [{[1/2]}, {[1/2]}]}, {[1], [{[3/2]}, {[{[1]}, {[{[1]}, {[4]}]}]}]}] = , [{[1]}, {[1]}] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[2](a[1] - 1, 2, 0, 0, 1), f[2](a[1], 0, 1, 0, 1)}, {f[3](a[1], 1, 0, 0, 1), f[5](a[1], 1, 0, 0) + [1]}] = , [{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}], [a[1]] }, {[a[1]], [{[a[1] + 1/2]}, {[{[a[1]]}, {[{[a[1]]}, {[4]}]}]}]} ] = , [{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 2} The value of the game = , [{f[2](0, 1, 1, 0, 1)}, {f[3](0, 2, 0, 0, 1), f[5](0, 2, 0, 0) + [1]}] = , [{[{[0]}, {[1]}]}, {[1/2], [{[5/4]}, {[3/4]}]}] = , [{[1/2]}, {[1/2]}] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[2](a[1] - 1, 3, 0, 0, 1), f[2](a[1], 1, 1, 0, 1)}, {f[3](a[1], 2, 0, 0, 1), f[5](a[1], 2, 0, 0) + [1]}] = , [{[a[1]], [{[2 a[1]]}, {[1 + a[1]]}]}, { [{[1 + a[1]]}, {[1 + a[1]]}], [ {[{[2 a[1] + 1]}, {[a[1] + 3/2]}]}, {[{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[1 + a[1]]}]}]}] = , [1 + a[1]] For the domain, {a[5] = 1, 3 <= a[2], a[3] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 0, 0, 1), f[2](a[1], a[2] - 1, 1, 0, 1)}, {f[3](a[1], a[2], 0, 0, 1), f[5](a[1], a[2], 0, 0) + [1]}] = , [{[a[1]], [%1, {[1 + a[1]]}]}, {[{[ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}], [{[{[2 a[1] + a[2] - 1]}, {[a[1] + 3/2]}]}, {[{[{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}, {[1 + a[1]]}]}]}] %1 := {[2 a[1] + a[2] - 2]} = , [1 + a[1]] For the domain, {a[5] = 1, 3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[2](0, a[2] - 1, 1, 0, 1)}, {f[3](0, a[2], 0, 0, 1), f[5](0, a[2], 0, 0) + [1]}] = , [{[{[-2 + a[2]]}, {[1]}]}, {[{[{ [{[-2 + a[2]]}, {[-2 + a[2]]}], [{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}]}, {[{[-2 + a[2]]}, {[1]}], [{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]} , {[1]}], [{[{[a[2] - 1]}, {[3/2]}]}, {[{[{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}, {[1]}]}]}] = , [1] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[1](0, 0, 0, 0, 2)}, {f[3](0, 0, 1, 0, 1), f[5](0, 0, 1, 0) + [1]}] = , [{[-3]}, {[0]}] = , [-1] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[2](0, 1, 1, 0, 1), f[1](1, 0, 0, 0, 2)}, {f[3](1, 0, 1, 0, 1), f[5](1, 0, 1, 0) + [1]}] = , [{[{[0]}, {[0]}], [{[0]}, {[1]}]}, {[3/2]}] = , [1] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [ {f[2](a[1] - 1, 1, 1, 0, 1), f[1](a[1], 0, 0, 0, 2)}, {f[3](a[1], 0, 1, 0, 1), f[5](a[1], 0, 1, 0) + [1]}] = , [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}], [{[2 a[1] - 2]}, {[a[1]]}] }, {[a[1] + 1/2]}] = , [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[1](a[1], a[2], 0, 0, 2), f[2](a[1] - 1, a[2] + 1, 1, 0, 1), f[2](a[1], a[2] - 1, 2, 0, 1)}, {f[3](a[1], a[2], 1, 0, 1), f[5](a[1], a[2], 1, 0) + [1]}] = , [{[2 a[1] + a[2] - 1], [{[2 a[1] + a[2] - 2]}, {[a[1]]}]}, {[1 + a[1]], [{[2 a[1] + a[2]]}, {[a[1] + 3/2]}]}] = , [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [ {f[1](0, a[2], 0, 0, 2), f[2](0, a[2] - 1, 2, 0, 1)}, {f[5](0, a[2], 1, 0) + [1], f[3](0, a[2], 1, 0, 1)}] = , [{[a[2] - 1]}, {[1], [{[a[2]]}, {[3/2]}]}] = , [{[a[2] - 1]}, {[1]}] For the domain, {a[5] = 1, a[4] = 0, 1 <= a[1], a[3] = 2, 1 <= a[2]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 2, 0, 1), f[2](a[1], a[2] - 1, 3, 0, 1), f[1](a[1], a[2], 1, 0, 2)}, {f[5](a[1], a[2], 2, 0) + [1]}] = , [{[{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}], [2 a[1] + a[2] - 1]} , {[1 + 2 a[1] + a[2]]}] = , [2 a[1] + a[2]] For the domain, {a[5] = 1, 3 <= a[3], a[4] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, a[3], 0, 1), f[2](a[1], a[2] - 1, a[3] + 1, 0, 1), f[1](a[1], a[2], a[3] - 1, 0, 2)}, {f[5](a[1], a[2], a[3], 0) + [1]}] = , [{[2 a[1] + a[2] - 1], [ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[1 + 2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}]}, {[1 + 2 a[1] + a[2]]}] = , [2 a[1] + a[2]] For the domain, {a[5] = 1, a[2] = 0, a[4] = 0, 1 <= a[1], a[3] = 2} The value of the game = , [ {f[2](a[1] - 1, 1, 2, 0, 1), f[1](a[1], 0, 1, 0, 2)}, {f[5](a[1], 0, 2, 0) + [1]}] = , [{[2 a[1] - 1]}, {[1 + 2 a[1]]}] = , [2 a[1]] For the domain, {a[5] = 1, 3 <= a[3], a[2] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{ f[2](a[1] - 1, 1, a[3], 0, 1), f[1](a[1], 0, a[3] - 1, 0, 2)} , {f[5](a[1], 0, a[3], 0) + [1]}] = , [{[2 a[1] - 1], [{[{[3 a[1] - 3 + a[3]]}, {[1 + 2 a[1]]}]}, {[2 a[1]]}]}, {[1 + 2 a[1]]}] = , [2 a[1]] For the domain, {a[5] = 1, a[1] = 0, a[4] = 0, a[3] = 2, 1 <= a[2]} The value of the game = , [ {f[2](0, a[2] - 1, 3, 0, 1), f[1](0, a[2], 1, 0, 2)}, {f[5](0, a[2], 2, 0) + [1]}] = , [{[{[a[2]]}, {[a[2]]}], [a[2] - 1]}, {[a[2] + 1]}] = , [a[2]] For the domain, {a[5] = 1, 3 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[2](0, a[2] - 1, a[3] + 1, 0, 1), f[1](0, a[2], a[3] - 1, 0, 2)}, {f[5](0, a[2], a[3], 0) + [1]}] = , [{[{[{[-3 + 2 a[2] + a[3]]}, {[a[2] + 1]}]}, {[a[2]]}], [a[2] - 1]}, {[a[2] + 1]}] = , [a[2]] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[4] = 0, a[3] = 2} The value of the game = , [{f[1](0, 0, 1, 0, 2)}, {f[5](0, 0, 2, 0) + [1]}] = , [{[-1]}, {[1]}] = , [0] For the domain, {a[5] = 1, 3 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[1](0, 0, a[3] - 1, 0, 2)}, {f[5](0, 0, a[3], 0) + [1]}] = , [{[{[{[a[3] - 3]}, {[1]}]}, {[0]}]}, {[1]}] = , [0] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[2](0, 1, 0, 1, 1), f[2](1, 0, 0, 0, 2)}, {f[5](1, 0, 0, 1) + [1], f[3](1, 0, 0, 1, 1)}] = , [{[0], [{[{[0]}, {[0]}]}, {[1/2]}]}, {[1], [5/4]}] = , [1/2] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[2](0, 1, 0, a[4], 1), f[2](1, 0, 0, a[4] - 1, 2)}, {f[5](1, 0, 0, a[4]) + [1], f[3](1, 0, 0, a[4], 1)}] = , [{[a[4] - 1], [{[{[a[4] - 1]}, {[a[4] - 1]}]}, {[1/2]}]}, {[1], [{[a[4]]}, {[3/2]}]}] = , [{[a[4] - 1]}, {[1]}] For the domain, {a[5] = 1, a[4] = 1, a[1] = 2, a[2] = 0, a[3] = 0} The value of the game = , [ {f[2](1, 1, 0, 1, 1), f[2](2, 0, 0, 0, 2)}, {f[5](2, 0, 0, 1) + [1], f[3](2, 0, 0, 1, 1)}] = , [{[2], [{[{[2]}, {[2]}]}, {[{[2]}, {[2]}]}]}, {[2], [{[3]}, {[5/2]}]}] = , [{[2]}, {[2]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 3} The value of the game = , [ {f[2](2, 1, 0, 1, 1), f[2](3, 0, 0, 0, 2)}, {f[5](3, 0, 0, 1) + [1], f[3](3, 0, 0, 1, 1)}] = , [{[4], [{[{[4]}, {[4]}]}, {[{[3]}, {[3]}]}]}, {[3], [{[5]}, {[7/2]}]}] = , [{[4]}, {[3]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 4} The value of the game = , [ {f[2](3, 1, 0, 1, 1), f[2](4, 0, 0, 0, 2)}, {f[3](4, 0, 0, 1, 1), f[5](4, 0, 0, 1) + [1]}] = , [{[6], [{[{[6]}, {[6]}]}, {[{[4]}, {[4]}]}]}, {[{[7]}, {[9/2]}], [4]}] = , [{[6]}, {[4]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, 5 <= a[1]} The value of the game = , [ {f[2](a[1] - 1, 1, 0, 1, 1), f[2](a[1], 0, 0, 0, 2)}, {f[3](a[1], 0, 0, 1, 1), f[5](a[1], 0, 0, 1) + [1]}] = , [{[2 a[1] - 2], [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[{[a[1]]}, {[a[1]]}]}]} , {[a[1]], [{[2 a[1] - 1]}, {[{[a[1]]}, {[6]}]}]}] = , [{[2 a[1] - 2]}, {[a[1]]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, a[3] = 0, 2 <= a[1]} The value of the game = , [{ f[2](a[1] - 1, 1, 0, a[4], 1), f[2](a[1], 0, 0, a[4] - 1, 2)} , {f[5](a[1], 0, 0, a[4]) + [1], f[3](a[1], 0, 0, a[4], 1)}] = , [{[{[{[2 a[1] + a[4] - 3]}, {[2 a[1] + a[4] - 3]}]}, {[{[a[1]]}, {[a[1]]}]}], [2 a[1] + a[4] - 3]}, {[a[1]], [{[2 a[1] + a[4] - 2]}, {[a[1] + 1/2]}]}] = , [{[2 a[1] + a[4] - 3]}, {[a[1]]}] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[2] = 1, 1 <= a[4]} The value of the game = , [ {f[2](0, 0, 1, a[4], 1), f[2](0, 1, 0, a[4] - 1, 2)}, {f[3](0, 1, 0, a[4], 1), f[5](0, 1, 0, a[4]) + [1]}] = , [{[{[a[4] - 1]}, {[a[4] - 1]}], [{[a[4] - 1]}, {[0]}]}, {[1/2], [{[a[4] - 1]}, {[1]}]}] = , [{[{[a[4] - 1]}, {[a[4] - 1]}]}, {[1/2]}] For the domain, {a[5] = 1, a[4] = 1, a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, 2, 0, 1, 1), f[2](a[1], 0, 1, 1, 1), f[2](a[1], 1, 0, 0, 2)}, {f[3](a[1], 1, 0, 1, 1), f[5](a[1], 1, 0, 1) + [1]}] = , [{[{[2 a[1]]}, {[2 a[1]]}], [{[2 a[1]]}, {[1 + a[1]]}], [ {[%1, %1], [%1, {[%1, {[1 + a[1]]}]}]}, {[%1, {[a[1]]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}], [{[2 a[1]]}, {[1 + a[1]]}]}] %1 := {[2 a[1] - 1]} = , [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] For the domain, {a[5] = 1, 2 <= a[4], a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, 2, 0, a[4], 1), f[2](a[1], 0, 1, a[4], 1), f[2](a[1], 1, 0, a[4] - 1, 2)}, {f[5](a[1], 1, 0, a[4]) + [1], f[3](a[1], 1, 0, a[4], 1)}] = , [{[%1, %1], [%1, {[1 + a[1]]}], [ {[{[2 a[1] + a[4] - 2]}, {[2 a[1] + a[4] - 2]}]}, {[{[{[2 a[1] - 1]}, {[1 + a[1]]}]}, {[a[1]]}]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}], [%1, {[1 + a[1]]}]}] %1 := {[2 a[1] - 1 + a[4]]} = , [{[{[2 a[1] - 1 + a[4]]}, {[2 a[1] - 1 + a[4]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] For the domain, {a[5] = 1, a[4] = 1, 2 <= a[2], a[3] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 0, 1, 1), f[2](a[1], a[2] - 1, 1, 1, 1), f[2](a[1], a[2], 0, 0, 2)}, {f[5](a[1], a[2], 0, 1) + [1], f[3](a[1], a[2], 0, 1, 1)}] = , [{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}], [ {[%2, %2], [%2, {[%2, {[1 + a[1]]}]}]}, {[{[%2, {[1 + a[1]]}]}, {[a[1]]}], [%2, {[a[1]]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}] %1 := {[2 a[1] + a[2] - 1]} %2 := {[2 a[1] + a[2] - 2]} = , [{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}] %1 := {[2 a[1] + a[2] - 1]} For the domain, {a[5] = 1, a[4] = 1, 2 <= a[2], a[1] = 0, a[3] = 0} The value of the game = , [ {f[2](0, a[2] - 1, 1, 1, 1), f[2](0, a[2], 0, 0, 2)}, {f[3](0, a[2], 0, 1, 1), f[5](0, a[2], 0, 1) + [1]}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}], [{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}, {[{[{[a[2] - 1]}, {[2]}]}, {[1]}], [{[a[2] - 1]}, {[1]}]}] For the domain, {a[5] = 1, 2 <= a[4], 2 <= a[2], a[3] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 0, a[4], 1), f[2](a[1], a[2] - 1, 1, a[4], 1), f[2](a[1], a[2], 0, a[4] - 1, 2)}, { f[3](a[1], a[2], 0, a[4], 1), f[5](a[1], a[2], 0, a[4]) + [1] }] = , [{[%1, %1], [%1, {[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}], [{ [{[2 a[1] + a[2] + a[4] - 3]}, {[2 a[1] + a[2] + a[4] - 3]}]} , {[{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}]}, { [{[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}], [%1, {[1 + a[1]]}]}] %1 := {[2 a[1] + a[2] + a[4] - 2]} = , [{[{[2 a[1] + a[2] + a[4] - 2]}, {[2 a[1] + a[2] + a[4] - 2]}] }, {[{[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}] For the domain, {a[5] = 1, 2 <= a[4], 2 <= a[2], a[1] = 0, a[3] = 0} The value of the game = , [{ f[2](0, a[2] - 1, 1, a[4], 1), f[2](0, a[2], 0, a[4] - 1, 2)} , {f[3](0, a[2], 0, a[4], 1), f[5](0, a[2], 0, a[4]) + [1]}] = , [{[%1, %1], [%1, {[{[a[2] - 1]}, {[2]}]}]}, {[{[{[a[2] - 1]}, {[2]}]}, {[1]}], [%1, {[1]}]}] %1 := {[-2 + a[2] + a[4]]} = , [{[{[-2 + a[2] + a[4]]}, {[-2 + a[2] + a[4]]}]}, {[{[{[a[2] - 1]}, {[2]}]}, {[1]}]}] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[2] = 0, 1 <= a[4]} The value of the game = , [{f[2](0, 0, 1, a[4] - 1, 2)}, {f[5](0, 0, 1, a[4]) + [1], f[3](0, 0, 1, a[4], 1)}] = , [{[a[4] - 1]}, {[0], [{[a[4]]}, {[1]}]}] = , [{[a[4] - 1]}, {[0]}] For the domain, {a[5] = 1, a[3] = 1, a[4] = 1, a[2] = 0, 1 <= a[1]} The value of the game = , [ {f[2](a[1], 0, 1, 0, 2), f[2](a[1] - 1, 1, 1, 1, 1)}, {f[5](a[1], 0, 1, 1) + [1], f[3](a[1], 0, 1, 1, 1)}] = , [{[2 a[1]], [{[2 a[1] - 1]}, {[{[2 a[1] - 1]}, {[1 + a[1]]}]}] }, {[1 + a[1]], [{[2 a[1] + 1]}, {[a[1] + 3/2]}]}] = , [{[2 a[1]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, 2 <= a[4], a[3] = 1, a[2] = 0, 1 <= a[1]} The value of the game = , [{ f[2](a[1], 0, 1, a[4] - 1, 2), f[2](a[1] - 1, 1, 1, a[4], 1)} , {f[5](a[1], 0, 1, a[4]) + [1], f[3](a[1], 0, 1, a[4], 1)}] = , [{[2 a[1] - 1 + a[4]], [{[2 a[1] + a[4] - 2]}, {[{[2 a[1] - 1]}, {[1 + a[1]]}]}]}, {[1 + a[1]], [{[2 a[1] + a[4]]}, {[a[1] + 3/2]}]}] = , [{[2 a[1] - 1 + a[4]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, a[3] = 1, 1 <= a[1], 1 <= a[2], 1 <= a[4]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 1, a[4], 1), f[2](a[1], a[2] - 1, 2, a[4], 1), f[2](a[1], a[2], 1, a[4] - 1, 2)}, { f[3](a[1], a[2], 1, a[4], 1), f[5](a[1], a[2], 1, a[4]) + [1] }] = , [{[a[4] + 2 a[1] + a[2] - 1], [{[2 a[1] + a[2] + a[4] - 2]}, {[{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}], [{[2 a[1] + a[2] + a[4] - 2]}, {[2 a[1] + a[2]]}]}, { [{[2 a[1] + a[2]]}, {[a[1] + 2]}], [{[a[4] + 2 a[1] + a[2]]}, {[a[1] + 2]}]}] = , [{[a[4] + 2 a[1] + a[2] - 1]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, 1 <= a[2], 1 <= a[4]} The value of the game = , [{ f[2](0, a[2] - 1, 2, a[4], 1), f[2](0, a[2], 1, a[4] - 1, 2)} , {f[5](0, a[2], 1, a[4]) + [1], f[3](0, a[2], 1, a[4], 1)}] = , [{[{[-2 + a[2] + a[4]]}, {[a[2]]}], [a[4] - 1 + a[2]]}, {[{[a[4] + a[2]]}, {[2]}], [{[a[2]]}, {[2]}]}] = , [{[a[4] - 1 + a[2]]}, {[{[a[2]]}, {[2]}]}] For the domain, {a[5] = 1, 2 <= a[3], 1 <= a[1], 1 <= a[2], 1 <= a[4]} The value of the game = , [{ f[2](a[1] - 1, a[2] + 1, a[3], a[4], 1), f[2](a[1], a[2], a[3], a[4] - 1, 2), f[2](a[1], a[2] - 1, a[3] + 1, a[4], 1)}, {f[5](a[1], a[2], a[3], a[4]) + [1]}] = , [{[a[4] + 2 a[1] + a[2] - 1], [{[2 a[1] + a[2] + a[4] - 2]}, {[2 a[1] + a[2]]}]}, {[1 + 2 a[1] + a[2]]}] = , [{[a[4] + 2 a[1] + a[2] - 1]}, {[1 + 2 a[1] + a[2]]}] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, 1 <= a[1], 1 <= a[4]} The value of the game = , [{f[2](a[1] - 1, 1, a[3], a[4], 1), f[2](a[1], 0, a[3], a[4] - 1, 2)}, {f[5](a[1], 0, a[3], a[4]) + [1]}] = , [{[2 a[1] - 1 + a[4]], [{[2 a[1] + a[4] - 2]}, {[2 a[1]]}]}, {[1 + 2 a[1]]}] = , [{[2 a[1] - 1 + a[4]]}, {[1 + 2 a[1]]}] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, 1 <= a[2], 1 <= a[4]} The value of the game = , [{f[2](0, a[2], a[3], a[4] - 1, 2), f[2](0, a[2] - 1, a[3] + 1, a[4], 1)}, {f[5](0, a[2], a[3], a[4]) + [1]}] = , [{[a[4] - 1 + a[2]], [{[-2 + a[2] + a[4]]}, {[a[2]]}]}, {[a[2] + 1]}] = , [{[a[4] - 1 + a[2]]}, {[a[2] + 1]}] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, 1 <= a[4]} The value of the game = , [{f[2](0, 0, a[3], a[4] - 1, 2)}, {f[5](0, 0, a[3], a[4]) + [1]}] = , [{[a[4] - 1]}, {[1]}] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [ {f[2](a[1] - 1, 1, 0, 0, a[5])}, {f[3](a[1], 0, 0, 0, a[5])}] = , [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[2 a[1] - 1]}] = , [2 a[1] - 2] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{}, {f[3](0, 0, 0, 0, a[5])}] = , [{}, {[-1]}] = , [-2] For the domain, {a[2] = 0, a[3] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](a[1], 0, 0, a[4] - 1, a[5] + 1), f[2](a[1] - 1, 1, 0, a[4], a[5])}, {f[3](a[1], 0, 0, a[4], a[5])}] = , [{[{[2 a[1] + a[4] - 2]}, {[2 a[1] + a[4] - 2]}], [2 a[1] + a[4] - 3]}, {[2 a[1] - 1 + a[4]]}] = , [2 a[1] + a[4] - 2] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](0, 0, 0, a[4] - 1, a[5] + 1)}, {f[3](0, 0, 0, a[4], a[5])}] = , [{[a[4] - 3]}, {[a[4] - 1]}] = , [-2 + a[4]] For the domain, {a[3] = 0, a[4] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 0, 0, a[5]), f[2](a[1], a[2] - 1, 1, 0, a[5])}, {f[3](a[1], a[2], 0, 0, a[5])}] = , [{[2 a[1] + a[2] - 1], [{[2 a[1] + a[2] - 2]}, {[2 a[1] + a[2] - 2]}]}, {[2 a[1] + a[2] - 1]}] = , [{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, 1 <= a[2], 2 <= a[5]} The value of the game = , [ {f[2](0, a[2] - 1, 1, 0, a[5])}, {f[3](0, a[2], 0, 0, a[5])}] = , [{[a[2] - 1]}, {[a[2] - 1]}] For the domain, {a[3] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[4]} The value of the game = , [{ f[2](a[1] - 1, a[2] + 1, 0, a[4], a[5]), f[2](a[1], a[2] - 1, 1, a[4], a[5]), f[2](a[1], a[2], 0, a[4] - 1, a[5] + 1)}, {f[3](a[1], a[2], 0, a[4], a[5])}] = , [{ [{[2 a[1] + a[2] + a[4] - 2]}, {[2 a[1] + a[2] + a[4] - 2]}], [a[4] + 2 a[1] + a[2] - 1]}, {[a[4] + 2 a[1] + a[2] - 1]}] = , [{[a[4] + 2 a[1] + a[2] - 1]}, {[a[4] + 2 a[1] + a[2] - 1]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](0, a[2] - 1, 1, a[4], a[5]), f[2](0, a[2], 0, a[4] - 1, a[5] + 1)}, {f[3](0, a[2], 0, a[4], a[5])}] = , [{[{[-2 + a[2] + a[4]]}, {[-2 + a[2] + a[4]]}], [a[4] - 1 + a[2]]}, {[a[4] - 1 + a[2]]}] = , [{[a[4] - 1 + a[2]]}, {[a[4] - 1 + a[2]]}] For the domain, {a[3] = 1, a[4] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[2](a[1], a[2] - 1, 2, 0, a[5]), f[2](a[1] - 1, a[2] + 1, 1, 0, a[5]), f[1](a[1], a[2], 0, 0, a[5] + 1)}, {f[3](a[1], a[2], 1, 0, a[5])}] = , [{[2 a[1] + a[2] - 1]}, {[1 + 2 a[1] + a[2]]}] = , [2 a[1] + a[2]] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [{ f[2](a[1] - 1, 1, 1, 0, a[5]), f[1](a[1], 0, 0, 0, a[5] + 1)} , {f[3](a[1], 0, 1, 0, a[5])}] = , [{[{[2 a[1] - 2]}, {[2 a[1] - 2]}], [2 a[1] - 1]}, {[2 a[1] + 1]}] = , [2 a[1]] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, 1 <= a[2], 2 <= a[5]} The value of the game = , [{ f[2](0, a[2] - 1, 2, 0, a[5]), f[1](0, a[2], 0, 0, a[5] + 1)} , {f[3](0, a[2], 1, 0, a[5])}] = , [{[a[2] - 1]}, {[a[2] + 1]}] = , [a[2]] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{f[1](0, 0, 0, 0, a[5] + 1)}, {f[3](0, 0, 1, 0, a[5])}] = , [{[-3]}, {[1]}] = , [0] For the domain, {a[3] = 1, 1 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[4]} The value of the game = , [{ f[2](a[1] - 1, a[2] + 1, 1, a[4], a[5]), f[2](a[1], a[2] - 1, 2, a[4], a[5]), f[2](a[1], a[2], 1, a[4] - 1, a[5] + 1)}, {f[3](a[1], a[2], 1, a[4], a[5])}] = , [{[a[4] + 2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] + 1 + a[4]]}] = , [a[4] + 2 a[1] + a[2]] For the domain, {a[3] = 1, a[2] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](a[1] - 1, 1, 1, a[4], a[5]), f[2](a[1], 0, 1, a[4] - 1, a[5] + 1)}, {f[3](a[1], 0, 1, a[4], a[5])}] = , [{[2 a[1] - 1 + a[4]]}, {[2 a[1] + 1 + a[4]]}] = , [a[4] + 2 a[1]] For the domain, {a[3] = 1, a[1] = 0, 1 <= a[2], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](0, a[2] - 1, 2, a[4], a[5]), f[2](0, a[2], 1, a[4] - 1, a[5] + 1)}, {f[3](0, a[2], 1, a[4], a[5])}] = , [{[a[4] - 1 + a[2]]}, {[1 + a[2] + a[4]]}] = , [a[4] + a[2]] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](0, 0, 1, a[4] - 1, a[5] + 1)}, {f[3](0, 0, 1, a[4], a[5])}] = , [{[a[4] - 1]}, {[a[4] + 1]}] = , [a[4]] For the domain, {a[4] = 0, 1 <= a[1], a[3] = 2, 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, 2, 0, a[5]), f[2](a[1], a[2] - 1, 3, 0, a[5]), f[1](a[1], a[2], 1, 0, a[5] + 1)}, {}] = , [{[{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}], [2 a[1] + a[2] - 1]} , {}] = , [2 a[1] + a[2]] For the domain, {3 <= a[3], a[4] = 0, 1 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{ f[2](a[1] - 1, a[2] + 1, a[3], 0, a[5]), f[2](a[1], a[2] - 1, a[3] + 1, 0, a[5]), f[1](a[1], a[2], a[3] - 1, 0, a[5] + 1)}, {}] = , [{[2 a[1] + a[2] - 1], [ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[1 + 2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}]}, {}] = , [2 a[1] + a[2]] For the domain, {a[2] = 0, a[4] = 0, 1 <= a[1], a[3] = 2, 2 <= a[5]} The value of the game = , [{ f[2](a[1] - 1, 1, 2, 0, a[5]), f[1](a[1], 0, 1, 0, a[5] + 1)} , {}] = , [{[2 a[1] - 1]}, {}] = , [2 a[1]] For the domain, {3 <= a[3], a[2] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [{f[2](a[1] - 1, 1, a[3], 0, a[5]), f[1](a[1], 0, a[3] - 1, 0, a[5] + 1)}, {}] = , [{[2 a[1] - 1], [{[{[3 a[1] - 3 + a[3]]}, {[1 + 2 a[1]]}]}, {[2 a[1]]}]}, {}] = , [2 a[1]] For the domain, {a[1] = 0, a[4] = 0, a[3] = 2, 1 <= a[2], 2 <= a[5]} The value of the game = , [{ f[2](0, a[2] - 1, 3, 0, a[5]), f[1](0, a[2], 1, 0, a[5] + 1)} , {}] = , [{[{[a[2]]}, {[a[2]]}], [a[2] - 1]}, {}] = , [a[2]] For the domain, {3 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[2](0, a[2] - 1, a[3] + 1, 0, a[5]), f[1](0, a[2], a[3] - 1, 0, a[5] + 1)}, {}] = , [{[{[{[-3 + 2 a[2] + a[3]]}, {[a[2] + 1]}]}, {[a[2]]}], [a[2] - 1]}, {}] = , [a[2]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[3] = 2, 2 <= a[5]} The value of the game = , [{f[1](0, 0, 1, 0, a[5] + 1)}, {}] = , [{[-1]}, {}] = , [0] For the domain, {3 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{f[1](0, 0, a[3] - 1, 0, a[5] + 1)}, {}] = , [{[{[{[a[3] - 3]}, {[1]}]}, {[0]}]}, {}] = , [0] For the domain, {2 <= a[3], 1 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[4]} The value of the game = , [{ f[2](a[1] - 1, a[2] + 1, a[3], a[4], a[5]), f[2](a[1], a[2] - 1, a[3] + 1, a[4], a[5]), f[2](a[1], a[2], a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[a[4] + 2 a[1] + a[2] - 1]}, {}] = , [a[4] + 2 a[1] + a[2]] For the domain, {2 <= a[3], a[2] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](a[1] - 1, 1, a[3], a[4], a[5]), f[2](a[1], 0, a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[2 a[1] - 1 + a[4]]}, {}] = , [a[4] + 2 a[1]] For the domain, {2 <= a[3], a[1] = 0, 1 <= a[2], 2 <= a[5], 1 <= a[4]} The value of the game = , [{ f[2](0, a[2] - 1, a[3] + 1, a[4], a[5]), f[2](0, a[2], a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[a[4] - 1 + a[2]]}, {}] = , [a[4] + a[2]] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](0, 0, a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[a[4] - 1]}, {}] = , [a[4]] ########## #, f[3], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{}, {f[4](0, 0, 0, 0, 0), f[6](0, 0, 0, 0) + [0]}] = , [{}, {[-3]}] = , [-4] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[3](0, 0, 0, 1, 0)}, {f[6](0, 0, 1, 0) + [0], f[4](0, 0, 1, 0, 0)}] = , [{[-2]}, {[0], [{[-1]}, {[-1]}]}] = , [-1] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[3](0, 0, a[3] - 1, 1, 0)}, {f[4](0, 0, a[3], 0, 0), f[6](0, 0, a[3], 0) + [0]}] = , [{[{[a[3] - 2]}, {[a[3] - 2]}]}, {[a[3] - 1], [{[a[3] - 2]}, {[a[3] - 2]}]}] = , [a[3] - 2] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{f[3](0, 0, 0, 0, 1)}, {f[4](0, 0, 0, 1, 0), f[6](0, 0, 0, 1) + [0]}] = , [{[-3]}, {[-1]}] = , [-2] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [ {f[3](0, 0, 0, 2, 0), f[3](0, 0, 1, 0, 1)}, {f[4](0, 0, 1, 1, 0), f[6](0, 0, 1, 1) + [0]}] = , [{[0], [{[{[-1]}, {[0]}]}, {[-1]}]}, {[0], [{[1]}, {[1]}]}] = , [{[0]}, {[0]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [ {f[3](0, 0, a[3] - 1, 2, 0), f[3](0, 0, a[3], 0, 1)}, {f[6](0, 0, a[3], 1) + [0], f[4](0, 0, a[3], 1, 0)}] = , [{[a[3] - 1], [{[{[2 a[3] - 3]}, {[a[3] - 1]}]}, {[a[3] - 2]}] }, {[a[3] - 1], [{[a[3]]}, {[a[3]]}]}] = , [{[a[3] - 1]}, {[a[3] - 1]}] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2} The value of the game = , [{f[3](0, 0, 0, 1, 1)}, {f[4](0, 0, 0, 2, 0), f[6](0, 0, 0, 2) + [0]}] = , [{[{[-1]}, {[0]}]}, {[-1], [{[{[0]}, {[1]}]}, {[0]}]}] = , [{[-1/2]}, {[-1]}] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0, 3 <= a[4]} The value of the game = , [{f[3](0, 0, 0, a[4] - 1, 1)}, {f[6](0, 0, 0, a[4]) + [0], f[4](0, 0, 0, a[4], 0)}] = , [{[{[a[4] - 3]}, {[0]}]}, {[-1], [{[{[-2 + a[4]]}, {[1]}]}, {[0]}]}] = , [{[{[a[4] - 3]}, {[0]}]}, {[-1]}] For the domain, {a[1] = 0, a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2} The value of the game = , [ {f[3](0, 0, a[3] - 1, 3, 0), f[3](0, 0, a[3], 1, 1)}, {f[6](0, 0, a[3], 2) + [0], f[4](0, 0, a[3], 2, 0)}] = , [{[{[2 a[3] - 1]}, {[a[3]]}], [{[{[2 a[3] - 2]}, {[a[3] - 1]}]}, {[a[3] - 2]}]}, {[a[3] - 1], [{[{[2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}]}] = , [{[{[2 a[3] - 1]}, {[a[3]]}]}, {[a[3] - 1]}] For the domain, {a[1] = 0, a[2] = 0, a[5] = 0, 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[3](0, 0, a[3] - 1, a[4] + 1, 0), f[3](0, 0, a[3], a[4] - 1, 1)}, {f[4](0, 0, a[3], a[4], 0), f[6](0, 0, a[3], a[4]) + [0]}] = , [{[{[2 a[3] + a[4] - 3]}, {[a[3]]}], [{[{[2 a[3] - 4 + a[4]]}, {[a[3] - 1]}]}, {[a[3] - 2]}]}, { [a[3] - 1], [{[{[2 a[3] + a[4] - 2]}, {[a[3] + 1]}]}, {[a[3]]}]}] = , [{[{[2 a[3] + a[4] - 3]}, {[a[3]]}]}, {[a[3] - 1]}] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[3](0, 1, 0, 0, 0)}, {f[6](1, 0, 0, 0) + [0], f[4](1, 0, 0, 0, 0)}] = , [{[-2]}, {[{[-1]}, {[-1]}]}] = , [-1] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 1, 0, 0, 0)}, {f[6](a[1], 0, 0, 0) + [0], f[4](a[1], 0, 0, 0, 0)}] = , [{[a[1] - 2]}, {[a[1] - 1], [{[a[1] - 2]}, {[3]}]}] = , [{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[2](0, 0, 0, 1, 0)}, {f[6](0, 1, 0, 0) + [0], f[4](0, 1, 0, 0, 0)}] = , [{[-3]}, {[-1], [{[0]}, {[0]}]}] = , [-2] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[3](0, 2, 0, 0, 0), f[2](1, 0, 0, 1, 0)}, {f[6](1, 1, 0, 0) + [0], f[4](1, 1, 0, 0, 0)}] = , [{[-1/2]}, {[{[1]}, {[1]}], [{[0]}, {[{[0]}, {[3]}]}]}] = , [0] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[3](a[1] - 1, 2, 0, 0, 0), f[2](a[1], 0, 0, 1, 0)}, {f[6](a[1], 1, 0, 0) + [0], f[4](a[1], 1, 0, 0, 0)}] = , [{[{[a[1] - 1]}, {[a[1] - 1]}]}, { [{[a[1]]}, {[a[1]]}], [{[a[1] - 1]}, {[{[a[1] - 1]}, {[3]}]}] }] = , [a[1] - 1] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 2} The value of the game = , [{f[2](0, 1, 0, 1, 0)}, {f[6](0, 2, 0, 0) + [0]}] = , [{[-1]}, {[-1/4]}] = , [-1/2] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 2} The value of the game = , [ {f[3](0, 3, 0, 0, 0), f[2](1, 1, 0, 1, 0)}, {f[6](1, 2, 0, 0) + [0]}] = , [{[1], [{[1/2]}, {[0]}]}, {[{[{[1]}, {[1]}]}, {[1]}]}] = , [{[1]}, {[1]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 2 <= a[1], a[2] = 2} The value of the game = , [ {f[2](a[1], 1, 0, 1, 0), f[3](a[1] - 1, 3, 0, 0, 0)}, {f[6](a[1], 2, 0, 0) + [0]}] = , [{[a[1]], [{[{[a[1]]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[{[{[a[1]]}, {[a[1]]}]}, {[a[1]]}]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 3} The value of the game = , [{f[2](0, 2, 0, 1, 0)}, {f[6](0, 3, 0, 0) + [0]}] = , [{[1/2]}, {[{[{[{[0]}, {[1]}]}, {[0]}]}, {[0]}]}] = , [{[1/2]}, {[0]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], 4 <= a[2]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, 0, 0, 0), f[2](a[1], a[2] - 1, 0, 1, 0)}, {f[6](a[1], a[2], 0, 0) + [0]}] = , [{[{[{[a[1]]}, {[a[1]]}]}, {[a[1] - 1]}], [{[1 + a[1]]}, {[1 + a[1]]}]}, {[ {[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}]}] = , [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, 4 <= a[2]} The value of the game = , [{f[2](0, a[2] - 1, 0, 1, 0)}, {f[6](0, a[2], 0, 0) + [0]}] = , [{[{[1]}, {[1]}]}, {[{[{[{[-3 + a[2]]}, {[1]}]}, {[0]}]}, {[0]}]}] = , [{[{[1]}, {[1]}]}, {[0]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, 1 <= a[1], a[2] = 3} The value of the game = , [ {f[3](a[1] - 1, 4, 0, 0, 0), f[2](a[1], 2, 0, 1, 0)}, {f[6](a[1], 3, 0, 0) + [0]}] = , [{[{[{[a[1]]}, {[a[1]]}]}, {[a[1] - 1]}], [{[1 + a[1]]}, {[1 + a[1]]}]}, {[{[{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}]}] = , [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[3](1, 0, 0, 1, 0), f[3](0, 1, 1, 0, 0)}, {f[4](1, 0, 1, 0, 0), f[6](1, 0, 1, 0) + [0]}] = , [{[0], [{[0]}, {[0]}]}, {[1]}] = , [1/2] For the domain, {a[3] = 1, a[1] = 2, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [ {f[3](2, 0, 0, 1, 0), f[3](1, 1, 1, 0, 0)}, {f[4](2, 0, 1, 0, 0), f[6](2, 0, 1, 0) + [0]}] = , [{[1], [{[3/2]}, {[3/2]}]}, {[2]}] = , [3/2] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 1, 1, 0, 0), f[3](3, 0, 0, 1, 0)}, {f[6](3, 0, 1, 0) + [0], f[4](3, 0, 1, 0, 0)}] = , [{[2], [{[5/2]}, {[5/2]}]}, {[3]}] = , [5/2] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 4} The value of the game = , [ {f[3](3, 1, 1, 0, 0), f[3](4, 0, 0, 1, 0)}, {f[6](4, 0, 1, 0) + [0], f[4](4, 0, 1, 0, 0)}] = , [{[3], [27/8]}, {[4]}] = , [7/2] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, 5 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 1, 1, 0, 0), f[3](a[1], 0, 0, 1, 0)}, {f[4](a[1], 0, 1, 0, 0), f[6](a[1], 0, 1, 0) + [0]}] = , [{[a[1] - 1], [{[a[1] - 1]}, {[{[a[1] - 1]}, {[5]}]}]}, {[a[1]]}] = , [a[1] - 1/2] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[3](1, 0, a[3] - 1, 1, 0), f[3](0, 1, a[3], 0, 0)}, {f[4](1, 0, a[3], 0, 0), f[6](1, 0, a[3], 0) + [0]}] = , [{[a[3] - 1], [{[- 1/2 + a[3]]}, {[- 1/2 + a[3]]}]}, {[a[3]]}] = , [- 1/2 + a[3]] For the domain, {2 <= a[3], a[1] = 2, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [ {f[3](1, 1, a[3], 0, 0), f[3](2, 0, a[3] - 1, 1, 0)}, {f[6](2, 0, a[3], 0) + [0], f[4](2, 0, a[3], 0, 0)}] = , [{[a[3]], [{[1/2 + a[3]]}, {[1/2 + a[3]]}]}, {[a[3] + 1]}] = , [1/2 + a[3]] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 1, a[3], 0, 0), f[3](3, 0, a[3] - 1, 1, 0)}, {f[4](3, 0, a[3], 0, 0), f[6](3, 0, a[3], 0) + [0]}] = , [{[{[3/2 + a[3]]}, {[3/2 + a[3]]}], [a[3] + 1]}, {[2 + a[3]]}] = , [3/2 + a[3]] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, a[5] = 0, 4 <= a[1]} The value of the game = , [{ f[3](a[1] - 1, 1, a[3], 0, 0), f[3](a[1], 0, a[3] - 1, 1, 0)} , {f[6](a[1], 0, a[3], 0) + [0], f[4](a[1], 0, a[3], 0, 0)}] = , [{[{[a[1] - 3/2 + a[3]]}, {[a[1] - 3/2 + a[3]]}], [a[1] - 2 + a[3]]}, {[a[1] + a[3] - 1]}] = , [a[1] - 3/2 + a[3]] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 1, 0, 1, 0), f[3](1, 0, 0, 0, 1)}, {f[6](1, 0, 0, 1) + [0], f[4](1, 0, 0, 1, 0)}] = , [{[0], [-1/2]}, {[0], [1/2]}] = , [{[0]}, {[0]}] For the domain, {a[4] = 1, a[1] = 2, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [ {f[3](1, 1, 0, 1, 0), f[3](2, 0, 0, 0, 1)}, {f[6](2, 0, 0, 1) + [0], f[4](2, 0, 0, 1, 0)}] = , [{[{[1]}, {[1]}], [{[1]}, {[{[1]}, {[4]}]}]}, {[3/2], [{[2]}, {[2]}]}] = , [{[3/2]}, {[3/2]}] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 1, 0, 1, 0), f[3](3, 0, 0, 0, 1)}, {f[4](3, 0, 0, 1, 0), f[6](3, 0, 0, 1) + [0]}] = , [{[{[2]}, {[2]}], [{[2]}, {[{[2]}, {[4]}]}]}, {[5/2], [{[3]}, {[3]}]}] = , [{[5/2]}, {[5/2]}] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 4} The value of the game = , [ {f[3](3, 1, 0, 1, 0), f[3](4, 0, 0, 0, 1)}, {f[6](4, 0, 0, 1) + [0], f[4](4, 0, 0, 1, 0)}] = , [{[{[3]}, {[3]}], [{[3]}, {[{[3]}, {[4]}]}]}, {[7/2], [{[4]}, {[4]}]}] = , [27/8] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, 5 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 1, 0, 1, 0), f[3](a[1], 0, 0, 0, 1)}, {f[6](a[1], 0, 0, 1) + [0], f[4](a[1], 0, 0, 1, 0)}] = , [{[{[a[1] - 1]}, {[a[1] - 1]}], [{[a[1] - 1]}, {[{[a[1] - 1]}, {[4]}]}]}, {[{[a[1]]}, {[a[1]]}], [{[a[1] - 1]}, {[5]}]}] = , [{[a[1] - 1]}, {[{[a[1] - 1]}, {[5]}]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{ f[3](0, 1, 1, 1, 0), f[3](1, 0, 1, 0, 1), f[3](1, 0, 0, 2, 0) }, {f[6](1, 0, 1, 1) + [0], f[4](1, 0, 1, 1, 0)}] = , [{[{[1]}, {[1]}], [3/2], [{[5/4]}, {[1/2]}]}, {[3/2], [{[2]}, {[2]}]}] = , [{[3/2]}, {[3/2]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 2, a[2] = 0, a[5] = 0} The value of the game = , [{ f[3](1, 1, 1, 1, 0), f[3](2, 0, 1, 0, 1), f[3](2, 0, 0, 2, 0) }, {f[4](2, 0, 1, 1, 0), f[6](2, 0, 1, 1) + [0]}] = , [{[5/2], [{[{[3]}, {[5/2]}]}, {[3/2]}], [{[2]}, {[2]}]}, {[5/2], [{[3]}, {[3]}]}] = , [{[5/2]}, {[5/2]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 3} The value of the game = , [{ f[3](2, 1, 1, 1, 0), f[3](3, 0, 1, 0, 1), f[3](3, 0, 0, 2, 0) }, {f[6](3, 0, 1, 1) + [0], f[4](3, 0, 1, 1, 0)}] = , [{[7/2], [{[{[5]}, {[7/2]}]}, {[5/2]}], [{[3]}, {[3]}]}, {[7/2], [{[4]}, {[4]}]}] = , [{[7/2]}, {[7/2]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 4} The value of the game = , [{ f[3](3, 1, 1, 1, 0), f[3](4, 0, 1, 0, 1), f[3](4, 0, 0, 2, 0) }, {f[6](4, 0, 1, 1) + [0], f[4](4, 0, 1, 1, 0)}] = , [{[9/2], [{[{[7]}, {[9/2]}]}, {[7/2]}], [{[4]}, {[4]}]}, {[9/2], [{[5]}, {[5]}]}] = , [{[9/2]}, {[9/2]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 5} The value of the game = , [{ f[3](5, 0, 0, 2, 0), f[3](4, 1, 1, 1, 0), f[3](5, 0, 1, 0, 1) }, {f[4](5, 0, 1, 1, 0), f[6](5, 0, 1, 1) + [0]}] = , [{[{[5]}, {[5]}], [11/2], [{[{[9]}, {[11/2]}]}, {[9/2]}]}, {[11/2], [{[6]}, {[6]}]}] = , [{[11/2]}, {[11/2]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 6} The value of the game = , [{ f[3](6, 0, 0, 2, 0), f[3](5, 1, 1, 1, 0), f[3](6, 0, 1, 0, 1) }, {f[6](6, 0, 1, 1) + [0], f[4](6, 0, 1, 1, 0)}] = , [{[{[6]}, {[6]}], [{[{[11]}, {[{[6]}, {[6]}]}]}, {[11/2]}], [13/2]}, {[13/2], [{[7]}, {[7]}]}] = , [{[13/2]}, {[13/2]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, 7 <= a[1]} The value of the game = , [{f[3](a[1], 0, 0, 2, 0), f[3](a[1] - 1, 1, 1, 1, 0), f[3](a[1], 0, 1, 0, 1)}, {f[6](a[1], 0, 1, 1) + [0], f[4](a[1], 0, 1, 1, 0)}] = , [{[a[1] + 1/2], [{[a[1]]}, {[a[1]]}], [{[a[1]]}, {[a[1] - 1/2]}]}, {[a[1] + 1/2], [{[1 + a[1]]}, {[1 + a[1]]}]}] = , [{[a[1] + 1/2]}, {[a[1] + 1/2]}] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 1, a[3], 1, 0), f[3](a[1], 0, a[3] - 1, 2, 0), f[3](a[1], 0, a[3], 0, 1)}, {f[6](a[1], 0, a[3], 1) + [0], f[4](a[1], 0, a[3], 1, 0)}] = , [{[a[1] - 1/2 + a[3]], [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}], [ {[{[2 a[1] - 3 + 2 a[3]]}, {[a[1] - 1/2 + a[3]]}]}, {[a[1] - 3/2 + a[3]]}]}, {[a[1] - 1/2 + a[3]], [{[a[1] + a[3]]}, {[a[1] + a[3]]}]}] = , [{[a[1] - 1/2 + a[3]]}, {[a[1] - 1/2 + a[3]]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1, a[4] = 2} The value of the game = , [ {f[3](0, 1, 0, 2, 0), f[3](1, 0, 0, 1, 1)}, {f[4](1, 0, 0, 2, 0), f[6](1, 0, 0, 2) + [0]}] = , [{[{[{[0]}, {[1]}]}, {[0]}], [5/4]}, {[{[{[2]}, {[2]}]}, {[1]}], [1/2]}] = , [{[5/4]}, {[1/2]}] For the domain, {a[1] = 2, a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2} The value of the game = , [ {f[3](1, 1, 0, 2, 0), f[3](2, 0, 0, 1, 1)}, {f[6](2, 0, 0, 2) + [0], f[4](2, 0, 0, 2, 0)}] = , [{[{[3]}, {[5/2]}], [{[{[2]}, {[2]}]}, {[1]}]}, {[{[{[4]}, {[3]}]}, {[2]}], [3/2]}] = , [{[{[3]}, {[5/2]}]}, {[3/2]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 3} The value of the game = , [ {f[3](2, 1, 0, 2, 0), f[3](3, 0, 0, 1, 1)}, {f[4](3, 0, 0, 2, 0), f[6](3, 0, 0, 2) + [0]}] = , [{[{[5]}, {[7/2]}], [{[{[4]}, {[3]}]}, {[2]}]}, {[5/2], [{[{[6]}, {[4]}]}, {[3]}]}] = , [{[{[5]}, {[7/2]}]}, {[5/2]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 4} The value of the game = , [ {f[3](3, 1, 0, 2, 0), f[3](4, 0, 0, 1, 1)}, {f[4](4, 0, 0, 2, 0), f[6](4, 0, 0, 2) + [0]}] = , [{[{[7]}, {[9/2]}], [{[{[6]}, {[4]}]}, {[3]}]}, {[7/2], [{[{[8]}, {[5]}]}, {[4]}]}] = , [{[{[7]}, {[9/2]}]}, {[7/2]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 5} The value of the game = , [ {f[3](4, 1, 0, 2, 0), f[3](5, 0, 0, 1, 1)}, {f[4](5, 0, 0, 2, 0), f[6](5, 0, 0, 2) + [0]}] = , [{[{[{[8]}, {[5]}]}, {[4]}], [{[9]}, {[{[5]}, {[6]}]}]}, {[9/2], [{[{[10]}, {[6]}]}, {[5]}]}] = , [{[{[9]}, {[11/2]}]}, {[9/2]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 6} The value of the game = , [ {f[3](5, 1, 0, 2, 0), f[3](6, 0, 0, 1, 1)}, {f[6](6, 0, 0, 2) + [0], f[4](6, 0, 0, 2, 0)}] = , [{[{[11]}, {[{[6]}, {[6]}]}], [{[{[10]}, {[6]}]}, {[5]}]}, {[11/2], [{[{[12]}, {[7]}]}, {[6]}]}] = , [{[{[11]}, {[{[6]}, {[6]}]}]}, {[11/2]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, 7 <= a[1]} The value of the game = , [ {f[3](a[1], 0, 0, 1, 1), f[3](a[1] - 1, 1, 0, 2, 0)}, {f[6](a[1], 0, 0, 2) + [0], f[4](a[1], 0, 0, 2, 0)}] = , [{[{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}], [{[2 a[1] - 1]}, {[{[a[1]]}, {[6]}]}]}, {[a[1] - 1/2], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}] = , [{[a[1]]}, {[a[1] - 1/2]}] For the domain, {a[2] = 0, a[5] = 0, a[1] = 1, 1 <= a[3], a[4] = 2} The value of the game = , [{f[3](0, 1, a[3], 2, 0), f[3](1, 0, a[3] - 1, 3, 0), f[3](1, 0, a[3], 1, 1)}, {f[6](1, 0, a[3], 2) + [0], f[4](1, 0, a[3], 2, 0)}] = , [{[{[{[2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}], [{[1 + 2 a[3]]}, {[3/2 + a[3]]}], [{[{[2 a[3]]}, {[1/2 + a[3]]}]}, {[- 1/2 + a[3]]}]}, { [{[{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}], [1/2 + a[3]]}] = , [{[{[1 + 2 a[3]]}, {[3/2 + a[3]]}]}, {[1/2 + a[3]]}] For the domain, {a[1] = 2, a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2} The value of the game = , [{f[3](1, 1, a[3], 2, 0), f[3](2, 0, a[3] - 1, 3, 0), f[3](2, 0, a[3], 1, 1)}, {f[6](2, 0, a[3], 2) + [0], f[4](2, 0, a[3], 2, 0)}] = , [{[{[3 + 2 a[3]]}, {[5/2 + a[3]]}], [{[{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}], [{[{[2 + 2 a[3]]}, {[3/2 + a[3]]}]}, {[1/2 + a[3]]}]}, { [{[{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}], [3/2 + a[3]]}] = , [{[{[3 + 2 a[3]]}, {[5/2 + a[3]]}]}, {[3/2 + a[3]]}] For the domain, {a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2, a[1] = 3} The value of the game = , [{f[3](2, 1, a[3], 2, 0), f[3](3, 0, a[3] - 1, 3, 0), f[3](3, 0, a[3], 1, 1)}, {f[4](3, 0, a[3], 2, 0), f[6](3, 0, a[3], 2) + [0]}] = , [{[{[5 + 2 a[3]]}, {[7/2 + a[3]]}], [{[{[4 + 2 a[3]]}, {[5/2 + a[3]]}]}, {[3/2 + a[3]]}], [{[{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}]}, { [{[{[6 + 2 a[3]]}, {[4 + a[3]]}]}, {[3 + a[3]]}], [5/2 + a[3]]}] = , [{[{[5 + 2 a[3]]}, {[7/2 + a[3]]}]}, {[5/2 + a[3]]}] For the domain, {a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2, 4 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 1, a[3], 2, 0), f[3](a[1], 0, a[3] - 1, 3, 0), f[3](a[1], 0, a[3], 1, 1)}, {f[4](a[1], 0, a[3], 2, 0), f[6](a[1], 0, a[3], 2) + [0]}] = , [{[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}], [ {[{[2 a[1] - 2 + 2 a[3]]}, {[a[1] - 1/2 + a[3]]}]}, {[a[1] - 3/2 + a[3]]}], [ {[{[2 a[1] - 2 + 2 a[3]]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}]}, {[a[1] - 1/2 + a[3]], [ {[{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]} ]}] = , [{[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, 1 <= a[1], 3 <= a[4]} The value of the game = , [{ f[3](a[1] - 1, 1, 0, a[4], 0), f[3](a[1], 0, 0, a[4] - 1, 1)} , {f[4](a[1], 0, 0, a[4], 0), f[6](a[1], 0, 0, a[4]) + [0]}] = , [{[{[{[2 a[1] + a[4] - 4]}, {[a[1]]}]}, {[a[1] - 1]}], [{[2 a[1] + a[4] - 3]}, {[a[1] + 1/2]}]}, {[a[1] - 1/2], [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}] = , [{[{[2 a[1] + a[4] - 3]}, {[a[1] + 1/2]}]}, {[a[1] - 1/2]}] For the domain, {a[2] = 0, a[5] = 0, 1 <= a[1], 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[3](a[1] - 1, 1, a[3], a[4], 0), f[3](a[1], 0, a[3] - 1, a[4] + 1, 0), f[3](a[1], 0, a[3], a[4] - 1, 1)}, { f[4](a[1], 0, a[3], a[4], 0), f[6](a[1], 0, a[3], a[4]) + [0] }] = , [{[{[{[2 a[1] + 2 a[3] - 4 + a[4]]}, {[a[1] - 1/2 + a[3]]}]}, {[a[1] - 3/2 + a[3]]}], [{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3] + 1/2]}], [ {[{[2 a[1] + 2 a[3] - 4 + a[4]]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}]}, {[a[1] - 1/2 + a[3]], [ {[{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]}]}] = , [{[{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[3](0, 2, 1, 0, 0), f[3](1, 1, 0, 1, 0)}, {f[6](1, 1, 1, 0) + [0], f[4](1, 1, 1, 0, 0)}] = , [{[0], [{[1]}, {[1]}]}, {[3], [3/2]}] = , [1] For the domain, {a[3] = 1, a[1] = 2, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[3](1, 2, 1, 0, 0), f[3](2, 1, 0, 1, 0)}, {f[4](2, 1, 1, 0, 0), f[6](2, 1, 1, 0) + [0]}] = , [{[1], [{[2]}, {[2]}]}, {[5/2], [4]}] = , [2] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, a[2] = 1, a[1] = 3} The value of the game = , [ {f[3](3, 1, 0, 1, 0), f[3](2, 2, 1, 0, 0)}, {f[6](3, 1, 1, 0) + [0], f[4](3, 1, 1, 0, 0)}] = , [{[2], [{[3]}, {[3]}]}, {[7/2], [9/2]}] = , [3] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 2, 1, 0, 0), f[3](a[1], 1, 0, 1, 0)}, {f[4](a[1], 1, 1, 0, 0), f[6](a[1], 1, 1, 0) + [0]}] = , [{[a[1] - 1], [{[a[1]]}, {[a[1]]}]}, {[a[1] + 1/2], [{[1 + a[1]]}, {[1 + a[1]]}]}] = , [a[1]] For the domain, {2 <= a[3], a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[3](0, 2, a[3], 0, 0), f[3](1, 1, a[3] - 1, 1, 0)}, {f[6](1, 1, a[3], 0) + [0], f[4](1, 1, a[3], 0, 0)}] = , [{[{[a[3]]}, {[a[3]]}], [a[3] - 1]}, {[1/2 + a[3]], [2 + a[3]]}] = , [a[3]] For the domain, {2 <= a[3], a[1] = 2, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[3](1, 2, a[3], 0, 0), f[3](2, 1, a[3] - 1, 1, 0)}, {f[4](2, 1, a[3], 0, 0), f[6](2, 1, a[3], 0) + [0]}] = , [{[a[3]], [{[a[3] + 1]}, {[a[3] + 1]}]}, {[3 + a[3]], [3/2 + a[3]]}] = , [a[3] + 1] For the domain, {2 <= a[3], a[4] = 0, a[5] = 0, a[2] = 1, a[1] = 3} The value of the game = , [ {f[3](2, 2, a[3], 0, 0), f[3](3, 1, a[3] - 1, 1, 0)}, {f[6](3, 1, a[3], 0) + [0], f[4](3, 1, a[3], 0, 0)}] = , [{[{[2 + a[3]]}, {[2 + a[3]]}], [a[3] + 1]}, {[4 + a[3]], [5/2 + a[3]]}] = , [2 + a[3]] For the domain, {2 <= a[3], a[4] = 0, a[5] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [{ f[3](a[1] - 1, 2, a[3], 0, 0), f[3](a[1], 1, a[3] - 1, 1, 0)} , {f[4](a[1], 1, a[3], 0, 0), f[6](a[1], 1, a[3], 0) + [0]}] = , [{ [a[1] - 2 + a[3]], [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}] }, {[a[1] - 1/2 + a[3]], [a[1] + 1 + a[3]]}] = , [a[1] + a[3] - 1] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[3](0, 1, 0, 1, 0)}, {f[6](0, 1, 1, 0) + [0], f[4](0, 1, 1, 0, 0)}] = , [{[-1/2]}, {[1/2], [2]}] = , [0] For the domain, {2 <= a[3], a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[3](0, 1, a[3] - 1, 1, 0)}, {f[4](0, 1, a[3], 0, 0), f[6](0, 1, a[3], 0) + [0]}] = , [{[{[a[3] - 1]}, {[a[3] - 1]}]}, {[- 1/2 + a[3]], [a[3] + 1]}] = , [a[3] - 1] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[3](a[1] - 1, 3, 1, 0, 0), f[3](a[1], 2, 0, 1, 0)}, {f[6](a[1], 2, 1, 0) + [0]}] = , [{[a[1] - 1], [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1] + 1/2]}] = , [a[1]] For the domain, {a[3] = 1, 3 <= a[2], a[4] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{ f[3](a[1] - 1, a[2] + 1, 1, 0, 0), f[3](a[1], a[2], 0, 1, 0)} , {f[6](a[1], a[2], 1, 0) + [0]}] = , [{[a[1] - 1], [{[{[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1] + 1/2]}] %1 := {[2 a[1] + a[2] - 2]} = , [a[1]] For the domain, {2 <= a[3], 2 <= a[2], a[4] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, a[3], 0, 0), f[3](a[1], a[2], a[3] - 1, 1, 0)}, {f[6](a[1], a[2], a[3], 0) + [0]}] = , [{ [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}], [a[1] - 2 + a[3]] }, {[a[1] - 1/2 + a[3]]}] = , [a[1] + a[3] - 1] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, a[5] = 0, a[2] = 2} The value of the game = , [{f[3](0, 2, 0, 1, 0)}, {f[6](0, 2, 1, 0) + [0]}] = , [{[{[1/2]}, {[0]}]}, {[1/2]}] = , [0] For the domain, {a[3] = 1, 3 <= a[2], a[1] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[3](0, a[2], 0, 1, 0)}, {f[6](0, a[2], 1, 0) + [0]}] = , [{[{[{[{[{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}], [{[-2 + a[2]]}, {[-2 + a[2]]}]}, {[{[{[-2 + a[2]]}, {[2]}]}, {[1]}], [{[-2 + a[2]]}, {[1]}]}]} , {[1]}]}, {[0]}]}, {[1/2]}] = , [0] For the domain, {2 <= a[3], 2 <= a[2], a[1] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[3](0, a[2], a[3] - 1, 1, 0)}, {f[6](0, a[2], a[3], 0) + [0]}] = , [{[{[a[3] - 1]}, {[a[3] - 1]}]}, {[- 1/2 + a[3]]}] = , [a[3] - 1] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[3](0, 1, 0, 0, 1), f[2](0, 0, 0, 2, 0)}, {f[6](0, 1, 0, 1) + [0], f[4](0, 1, 0, 1, 0)}] = , [{[-1], [{[{[-2]}, {[-1]}]}, {[-2]}]}, {[0], [1]}] = , [-1/2] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{ f[3](0, 2, 0, 1, 0), f[3](1, 1, 0, 0, 1), f[2](1, 0, 0, 2, 0) }, {f[6](1, 1, 0, 1) + [0], f[4](1, 1, 0, 1, 0)}] = , [{[1], [{[1/2]}, {[0]}], [{[{[0]}, {[1]}]}, {[0]}]}, {[1], [2]}] = , [{[1]}, {[1]}] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [{f[2](a[1], 0, 0, 2, 0), f[3](a[1], 1, 0, 0, 1), f[3](a[1] - 1, 2, 0, 1, 0)}, {f[4](a[1], 1, 0, 1, 0), f[6](a[1], 1, 0, 1) + [0]}] = , [{[a[1]], [{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}], [{[{[a[1]]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]], [1 + a[1]]} ] = , [{[a[1]]}, {[a[1]]}] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 2} The value of the game = , [ {f[2](0, 1, 0, 2, 0), f[3](0, 2, 0, 0, 1)}, {f[6](0, 2, 0, 1) + [0]}] = , [{[1/2], [{[{[{[0]}, {[0]}]}, {[1/2]}]}, {[-1/2]}]}, {[0]}] = , [{[1/2]}, {[0]}] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [{f[3](a[1] - 1, 3, 0, 1, 0), f[2](a[1], 1, 0, 2, 0), f[3](a[1], 2, 0, 0, 1)}, {f[6](a[1], 2, 0, 1) + [0]}] = , [{[{[1 + a[1]]}, {[1 + a[1]]}], [{ [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} , {[{[a[1]]}, {[a[1]]}]}], [{[{[ {[%1, %1], [%1, {[%1, {[1 + a[1]]}]}]}, {[%1, {[a[1]]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}]}]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] %1 := {[2 a[1] - 1]} = , [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[4] = 1, 3 <= a[2], a[3] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, 0, 1, 0), f[2](a[1], a[2] - 1, 0, 2, 0), f[3](a[1], a[2], 0, 0, 1)}, {f[6](a[1], a[2], 0, 1) + [0]}] = , [{[{[{[%2, %2], [%2, %3]}, {[%2, {[1 + a[1]]}], [%3, {[1 + a[1]]}]}]}, {[1 + a[1]]}], [{ [{[%2, %2], [%2, %3]}, {[%2, {[1 + a[1]]}], [%3, {[1 + a[1]]}]}]}, {[{[%1, {[1 + a[1]]}]}, {[a[1]]}]}], [{[{[ {[%1, %1], [%1, {[%1, {[1 + a[1]]}]}]}, {[{[%1, {[1 + a[1]]}]}, {[a[1]]}], [%1, {[a[1]]}]}]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] %1 := {[2 a[1] + a[2] - 3]} %2 := {[2 a[1] + a[2] - 2]} %3 := {[%2, {[a[1] + 2]}]} = , [{[{[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}]}, {[a[1]]}] %1 := {[2 a[1] + a[2] - 2]} For the domain, {a[4] = 1, 3 <= a[2], a[1] = 0, a[3] = 0, a[5] = 0} The value of the game = , [ {f[2](0, a[2] - 1, 0, 2, 0), f[3](0, a[2], 0, 0, 1)}, {f[6](0, a[2], 0, 1) + [0]}] = , [{[{[{[{[-2 + a[2]]}, {[-2 + a[2]]}], [{[-2 + a[2]]}, %1]}, {[{[-2 + a[2]]}, {[1]}], [%1, {[1]}]}]}, {[1]}], [{[ {[{[-2 + a[2]]}, {[-2 + a[2]]}], [{[-2 + a[2]]}, %1]}, {[{[-2 + a[2]]}, {[1]}], [%1, {[1]}]}]}, {[{[{[-3 + a[2]]}, {[1]}]}, {[0]}]}]}, {[0]}] %1 := {[{[-2 + a[2]]}, {[2]}]} = , [{[{[{[{[-2 + a[2]]}, {[-2 + a[2]]}], [{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}]}, {[{[-2 + a[2]]}, {[1]}], [{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]} , {[1]}]}, {[0]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{ f[3](0, 2, 1, 1, 0), f[3](1, 1, 0, 2, 0), f[3](1, 1, 1, 0, 1) }, {f[6](1, 1, 1, 1) + [0], f[4](1, 1, 1, 1, 0)}] = , [{[{[1]}, {[1]}], [2], [{[{[2]}, {[2]}]}, {[1]}]}, {[2], [{[4]}, {[4]}]}] = , [{[2]}, {[2]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 2, a[5] = 0, a[2] = 1} The value of the game = , [{ f[3](2, 1, 0, 2, 0), f[3](1, 2, 1, 1, 0), f[3](2, 1, 1, 0, 1) }, {f[6](2, 1, 1, 1) + [0], f[4](2, 1, 1, 1, 0)}] = , [{[3], [{[2]}, {[2]}], [{[{[4]}, {[3]}]}, {[2]}]}, {[3], [{[5]}, {[5]}]}] = , [{[3]}, {[3]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, a[2] = 1, a[1] = 3} The value of the game = , [{ f[3](3, 1, 0, 2, 0), f[3](2, 2, 1, 1, 0), f[3](3, 1, 1, 0, 1) }, {f[6](3, 1, 1, 1) + [0], f[4](3, 1, 1, 1, 0)}] = , [{[4], [{[{[6]}, {[4]}]}, {[3]}], [{[3]}, {[3]}]}, {[4], [23/4]}] = , [{[4]}, {[4]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [{f[3](a[1], 1, 0, 2, 0), f[3](a[1] - 1, 2, 1, 1, 0), f[3](a[1], 1, 1, 0, 1)}, {f[6](a[1], 1, 1, 1) + [0], f[4](a[1], 1, 1, 1, 0)}] = , [{[1 + a[1]], [{[a[1]]}, {[a[1]]}], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[1 + a[1]], [a[1] + 2]}] = , [{[1 + a[1]]}, {[1 + a[1]]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 2, a[3], 1, 0), f[3](a[1], 1, a[3] - 1, 2, 0), f[3](a[1], 1, a[3], 0, 1)}, {f[4](a[1], 1, a[3], 1, 0), f[6](a[1], 1, a[3], 1) + [0]}] = , [{[{[{[2 a[1] - 2 + 2 a[3]]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}], [a[1] + a[3]], [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}]}, {[{[a[1] + 2 + a[3]]}, {[a[1] + 2 + a[3]]}], [a[1] + a[3]]}] = , [{[a[1] + a[3]]}, {[a[1] + a[3]]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[3](0, 1, 0, 2, 0), f[3](0, 1, 1, 0, 1)}, {f[4](0, 1, 1, 1, 0), f[6](0, 1, 1, 1) + [0]}] = , [{[1], [{[{[0]}, {[1]}]}, {[0]}]}, {[1], [{[3]}, {[3]}]}] = , [{[1]}, {[1]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[3](0, 1, a[3] - 1, 2, 0), f[3](0, 1, a[3], 0, 1)}, {f[4](0, 1, a[3], 1, 0), f[6](0, 1, a[3], 1) + [0]}] = , [{[a[3]], [{[{[-2 + 2 a[3]]}, {[a[3]]}]}, {[a[3] - 1]}]}, {[a[3]], [{[2 + a[3]]}, {[2 + a[3]]}]}] = , [{[a[3]]}, {[a[3]]}] For the domain, {a[4] = 1, 2 <= a[2], a[5] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, a[3], 1, 0), f[3](a[1], a[2], a[3] - 1, 2, 0), f[3](a[1], a[2], a[3], 0, 1)}, {f[6](a[1], a[2], a[3], 1) + [0]}] = , [{[{[{[2 a[1] + a[2] + 2 a[3] - 3]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}], [a[1] + a[3]], [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}]}, {[a[1] + a[3]]}] = , [{[a[1] + a[3]]}, {[a[1] + a[3]]}] For the domain, {a[4] = 1, 2 <= a[2], a[1] = 0, a[5] = 0, 1 <= a[3]} The value of the game = , [ {f[3](0, a[2], a[3] - 1, 2, 0), f[3](0, a[2], a[3], 0, 1)}, {f[6](0, a[2], a[3], 1) + [0]}] = , [{[a[3]], [{[{[-3 + a[2] + 2 a[3]]}, {[a[3]]}]}, {[a[3] - 1]}] }, {[a[3]]}] = , [{[a[3]]}, {[a[3]]}] For the domain, {a[3] = 0, a[5] = 0, a[1] = 1, a[2] = 1, a[4] = 2} The value of the game = , [{ f[3](0, 2, 0, 2, 0), f[3](1, 1, 0, 1, 1), f[2](1, 0, 0, 3, 0) }, {f[6](1, 1, 0, 2) + [0], f[4](1, 1, 0, 2, 0)}] = , [{[{[{[1]}, {[1]}]}, {[0]}], [{[2]}, {[2]}]}, {[1], [{[{[5]}, {[4]}]}, {[3]}]}] = , [{[{[2]}, {[2]}]}, {[1]}] For the domain, {a[1] = 2, a[3] = 0, a[5] = 0, a[2] = 1, a[4] = 2} The value of the game = , [{ f[3](1, 2, 0, 2, 0), f[2](2, 0, 0, 3, 0), f[3](2, 1, 0, 1, 1) }, {f[6](2, 1, 0, 2) + [0], f[4](2, 1, 0, 2, 0)}] = , [{[{[{[3]}, {[2]}]}, {[1]}], [{[4]}, {[3]}]}, {[{[{[7]}, {[5]}]}, {[4]}], [2]}] = , [{[{[4]}, {[3]}]}, {[2]}] For the domain, {a[3] = 0, a[5] = 0, a[2] = 1, a[4] = 2, a[1] = 3} The value of the game = , [{ f[3](2, 2, 0, 2, 0), f[2](3, 0, 0, 3, 0), f[3](3, 1, 0, 1, 1) }, {f[6](3, 1, 0, 2) + [0], f[4](3, 1, 0, 2, 0)}] = , [{[{[6]}, {[4]}], [{[{[5]}, {[3]}]}, {[2]}]}, {[3], [{[{[9]}, {[11/2]}]}, {[5]}]}] = , [{[{[6]}, {[4]}]}, {[3]}] For the domain, {a[3] = 0, a[5] = 0, a[2] = 1, a[4] = 2, 4 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 2, 0, 2, 0), f[2](a[1], 0, 0, 3, 0), f[3](a[1], 1, 0, 1, 1)}, {f[6](a[1], 1, 0, 2) + [0], f[4](a[1], 1, 0, 2, 0)}] = , [{[{[2 a[1]]}, {[1 + a[1]]}], [{[{[2 a[1] - 1]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]], [{[a[1] + 2]}, {[a[1] + 2]}]}] = , [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[3] = 0, a[5] = 0, a[2] = 1, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[3](a[1] - 1, 2, 0, a[4], 0), f[2](a[1], 0, 0, a[4] + 1, 0), f[3](a[1], 1, 0, a[4] - 1, 1)} , {f[4](a[1], 1, 0, a[4], 0), f[6](a[1], 1, 0, a[4]) + [0]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}], [{[{[2 a[1] + a[4] - 3]}, {[a[1]]}]}, {[a[1] - 1]}]}, { [a[1]], [{[{[2 a[1] + 1 + a[4]]}, {[a[1] + 3]}]}, {[a[1] + 2]}]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 1, a[4] = 2} The value of the game = , [ {f[2](0, 0, 0, 3, 0), f[3](0, 1, 0, 1, 1)}, {f[6](0, 1, 0, 2) + [0], f[4](0, 1, 0, 2, 0)}] = , [{[{[{[-1]}, {[-1]}]}, {[-2]}], [{[0]}, {[1]}]}, {[0], [{[{[3]}, {[3]}]}, {[2]}]}] = , [{[1/2]}, {[0]}] For the domain, {a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 1, 3 <= a[4]} The value of the game = , [ {f[2](0, 0, 0, a[4] + 1, 0), f[3](0, 1, 0, a[4] - 1, 1)}, {f[6](0, 1, 0, a[4]) + [0], f[4](0, 1, 0, a[4], 0)}] = , [{[{[-2 + a[4]]}, {[1]}], [{[{[a[4] - 3]}, {[-1]}]}, {[-2]}]}, {[0], [{[{[a[4] + 1]}, {[3]}]}, {[2]}]}] = , [{[{[-2 + a[4]]}, {[1]}]}, {[0]}] For the domain, {a[5] = 0, a[1] = 1, a[2] = 1, 1 <= a[3], a[4] = 2} The value of the game = , [{f[3](1, 1, a[3] - 1, 3, 0), f[3](1, 1, a[3], 1, 1), f[3](0, 2, a[3], 2, 0)}, {f[6](1, 1, a[3], 2) + [0], f[4](1, 1, a[3], 2, 0)}] = , [{[{[2 a[3] + 2]}, {[2 + a[3]]}], [{[{[1 + 2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}]}, { [a[3] + 1], [{[{[5 + 2 a[3]]}, {[4 + a[3]]}]}, {[3 + a[3]]}]} ] = , [{[{[2 a[3] + 2]}, {[2 + a[3]]}]}, {[a[3] + 1]}] For the domain, {a[1] = 2, a[5] = 0, a[2] = 1, 1 <= a[3], a[4] = 2} The value of the game = , [{f[3](2, 1, a[3] - 1, 3, 0), f[3](2, 1, a[3], 1, 1), f[3](1, 2, a[3], 2, 0)}, {f[6](2, 1, a[3], 2) + [0], f[4](2, 1, a[3], 2, 0)}] = , [{[{[4 + 2 a[3]]}, {[3 + a[3]]}], [{[{[3 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}]}, { [2 + a[3]], [{[{[7 + 2 a[3]]}, {[5 + a[3]]}]}, {[4 + a[3]]}]} ] = , [{[{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}] For the domain, {a[5] = 0, a[2] = 1, 1 <= a[3], a[4] = 2, a[1] = 3} The value of the game = , [{f[3](2, 2, a[3], 2, 0), f[3](3, 1, a[3] - 1, 3, 0), f[3](3, 1, a[3], 1, 1)}, {f[6](3, 1, a[3], 2) + [0], f[4](3, 1, a[3], 2, 0)}] = , [{[{[{[5 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}], [{[6 + 2 a[3]]}, {[4 + a[3]]}]}, { [3 + a[3]], [{[{[9 + 2 a[3]]}, {[6 + a[3]]}]}, {[5 + a[3]]}]} ] = , [{[{[6 + 2 a[3]]}, {[4 + a[3]]}]}, {[3 + a[3]]}] For the domain, {a[5] = 0, a[2] = 1, 1 <= a[3], a[4] = 2, 4 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 2, a[3], 2, 0), f[3](a[1], 1, a[3] - 1, 3, 0), f[3](a[1], 1, a[3], 1, 1)}, {f[6](a[1], 1, a[3], 2) + [0], f[4](a[1], 1, a[3], 2, 0)}] = , [{[{[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}], [{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]], [{[{[2 a[1] + 3 + 2 a[3]]}, {[a[1] + 3 + a[3]]}]}, {[a[1] + 2 + a[3]]}]}] = , [{[{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]} ] For the domain, {a[5] = 0, a[2] = 1, 1 <= a[1], 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[3](a[1] - 1, 2, a[3], a[4], 0), f[3](a[1], 1, a[3] - 1, a[4] + 1, 0), f[3](a[1], 1, a[3], a[4] - 1, 1)}, { f[6](a[1], 1, a[3], a[4]) + [0], f[4](a[1], 1, a[3], a[4], 0) }] = , [{[{[{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}], [{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + 1 + a[3]]}]}, {[ {[{[2 a[1] + 1 + 2 a[3] + a[4]]}, {[a[1] + 3 + a[3]]}]}, {[a[1] + 2 + a[3]]}], [a[1] + a[3]]}] = , [{[{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]}] For the domain, {a[1] = 0, a[5] = 0, a[2] = 1, 1 <= a[3], a[4] = 2} The value of the game = , [ {f[3](0, 1, a[3] - 1, 3, 0), f[3](0, 1, a[3], 1, 1)}, {f[6](0, 1, a[3], 2) + [0], f[4](0, 1, a[3], 2, 0)}] = , [{[{[{[2 a[3] - 1]}, {[a[3]]}]}, {[a[3] - 1]}], [{[2 a[3]]}, {[a[3] + 1]}]}, {[{[{[3 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}], [a[3]]}] = , [{[{[2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}] For the domain, {a[1] = 0, a[5] = 0, a[2] = 1, 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[3](0, 1, a[3] - 1, a[4] + 1, 0), f[3](0, 1, a[3], a[4] - 1, 1)}, {f[6](0, 1, a[3], a[4]) + [0], f[4](0, 1, a[3], a[4], 0)}] = , [{[{[2 a[3] + a[4] - 2]}, {[a[3] + 1]}], [{[{[2 a[3] + a[4] - 3]}, {[a[3]]}]}, {[a[3] - 1]}]}, { [a[3]], [{[{[1 + 2 a[3] + a[4]]}, {[3 + a[3]]}]}, {[2 + a[3]]}]}] = , [{[{[2 a[3] + a[4] - 2]}, {[a[3] + 1]}]}, {[a[3]]}] For the domain, {2 <= a[4], a[3] = 0, a[5] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [{f[3](a[1] - 1, 3, 0, a[4], 0), f[2](a[1], 1, 0, a[4] + 1, 0), f[3](a[1], 2, 0, a[4] - 1, 1)} , {f[6](a[1], 2, 0, a[4]) + [0]}] = , [{[{[{[{[2 a[1] - 1 + a[4]]}, {[2 a[1] - 1 + a[4]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}, {[{[a[1]]}, {[a[1]]}]}], [{[2 a[1] - 1 + a[4]]}, {[1 + a[1]]}], [{[{[2 a[1] + a[4] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[{[2 a[1] - 1 + a[4]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {2 <= a[4], 3 <= a[2], a[3] = 0, a[5] = 0, 1 <= a[1]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, 0, a[4], 0), f[2](a[1], a[2] - 1, 0, a[4] + 1, 0), f[3](a[1], a[2], 0, a[4] - 1, 1)}, {f[6](a[1], a[2], 0, a[4]) + [0]}] = , [{[%1, {[1 + a[1]]}], [{[{[2 a[1] - 4 + a[2] + a[4]]}, {[a[1]]}]}, {[a[1] - 1]}], [ {[{[%1, %1]}, {[{[{[2 a[1] + a[2] - 2]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}]}, {[a[1]]}] %1 := {[2 a[1] + a[2] + a[4] - 3]} = , [{[{[2 a[1] + a[2] + a[4] - 3]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {2 <= a[4], a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 2} The value of the game = , [ {f[2](0, 1, 0, a[4] + 1, 0), f[3](0, 2, 0, a[4] - 1, 1)}, {f[6](0, 2, 0, a[4]) + [0]}] = , [{[{[{[{[a[4] - 1]}, {[a[4] - 1]}]}, {[1/2]}]}, {[-1/2]}], [{[a[4] - 1]}, {[1]}]}, {[0]}] = , [{[{[a[4] - 1]}, {[1]}]}, {[0]}] For the domain, {2 <= a[4], 3 <= a[2], a[1] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{f[3](0, a[2], 0, a[4] - 1, 1), f[2](0, a[2] - 1, 0, a[4] + 1, 0)}, {f[6](0, a[2], 0, a[4]) + [0]}] = , [{[{[{[{[-3 + a[2] + a[4]]}, {[-3 + a[2] + a[4]]}]}, {[{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]}, {[{[{[-3 + a[2]]}, {[1]}]}, {[0]}]}], [{[-3 + a[2] + a[4]]}, {[1]}]}, {[0]}] = , [{[{[-3 + a[2] + a[4]]}, {[1]}]}, {[0]}] For the domain, {2 <= a[4], 2 <= a[2], a[5] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{ f[3](a[1] - 1, a[2] + 1, a[3], a[4], 0), f[3](a[1], a[2], a[3], a[4] - 1, 1), f[3](a[1], a[2], a[3] - 1, a[4] + 1, 0)}, {f[6](a[1], a[2], a[3], a[4]) + [0]}] = , [{ [{[2 a[1] + a[2] + 2 a[3] + a[4] - 3]}, {[a[1] + 1 + a[3]]}], [{[{[2 a[1] - 4 + a[2] + 2 a[3] + a[4]]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}]}, {[a[1] + a[3]]}] = , [{[{[2 a[1] + a[2] + 2 a[3] + a[4] - 3]}, {[a[1] + 1 + a[3]]}] }, {[a[1] + a[3]]}] For the domain, {2 <= a[4], 2 <= a[2], a[1] = 0, a[5] = 0, 1 <= a[3]} The value of the game = , [{f[3](0, a[2], a[3], a[4] - 1, 1), f[3](0, a[2], a[3] - 1, a[4] + 1, 0)}, {f[6](0, a[2], a[3], a[4]) + [0]}] = , [{[{[-3 + a[2] + 2 a[3] + a[4]]}, {[a[3] + 1]}], [{[{[-4 + a[2] + 2 a[3] + a[4]]}, {[a[3]]}]}, {[a[3] - 1]}]}, {[a[3]]}] = , [{[{[-3 + a[2] + 2 a[3] + a[4]]}, {[a[3] + 1]}]}, {[a[3]]}] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{}, {f[4](0, 0, 0, 0, 1), f[6](0, 0, 0, 0) + [1]}] = , [{}, {[-2]}] = , [-3] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[4] = 0, 1 <= a[3]} The value of the game = , [{f[3](0, 0, a[3] - 1, 1, 1)}, {f[4](0, 0, a[3], 0, 1), f[6](0, 0, a[3], 0) + [1]}] = , [{[{[2 a[3] - 3]}, {[a[3] - 1]}]}, {[{[a[3] - 1]}, {[a[3] - 1]}], [a[3]]}] = , [a[3] - 1] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[3](0, 0, a[3] - 1, 1, 1)}, {f[4](0, 0, a[3], 0, 1), f[6](0, 0, a[3], 0) + [1]}] = , [{[{[2 a[3] - 3]}, {[a[3] - 1]}]}, {[{[a[3] - 1]}, {[a[3] - 1]}], [a[3]]}] = , [a[3] - 1] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{f[3](0, 0, 0, 0, 2)}, {f[6](0, 0, 0, 1) + [1], f[4](0, 0, 0, 1, 1)}] = , [{[-1]}, {[0], [{[0]}, {[1]}]}] = , [-1/2] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{f[3](0, 0, 0, a[4] - 1, 2)}, {f[6](0, 0, 0, a[4]) + [1], f[4](0, 0, 0, a[4], 1)}] = , [{[-2 + a[4]]}, {[0], [{[a[4] - 1]}, {[1]}]}] = , [{[-2 + a[4]]}, {[0]}] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[2] = 0, 1 <= a[3]} The value of the game = , [ {f[3](0, 0, a[3], 0, 2), f[3](0, 0, a[3] - 1, 2, 1)}, {f[6](0, 0, a[3], 1) + [1], f[4](0, 0, a[3], 1, 1)}] = , [{[{[2 a[3] - 2]}, {[a[3] - 1]}], [2 a[3] - 1]}, {[a[3]], [{[2 a[3]]}, {[a[3] + 1]}]}] = , [{[2 a[3] - 1]}, {[a[3]]}] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[2] = 0, 1 <= a[3]} The value of the game = , [{f[3](0, 0, a[3] - 1, a[4] + 1, 1), f[3](0, 0, a[3], a[4] - 1, 2)}, {f[4](0, 0, a[3], a[4], 1), f[6](0, 0, a[3], a[4]) + [1]}] = , [{[2 a[3] + a[4] - 2], [{[2 a[3] + a[4] - 3]}, {[a[3] - 1]}]}, {[a[3]], [{[-1 + 2 a[3] + a[4]]}, {[a[3] + 1]}]}] = , [{[2 a[3] + a[4] - 2]}, {[a[3]]}] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[3](0, 1, 0, 0, 1)}, {f[6](1, 0, 0, 0) + [1], f[4](1, 0, 0, 0, 1)}] = , [{[-1]}, {[{[0]}, {[0]}]}] = , [0] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 1, 0, 0, 1)}, {f[6](a[1], 0, 0, 0) + [1], f[4](a[1], 0, 0, 0, 1)}] = , [{[a[1] - 1]}, {[a[1]], [{[a[1] - 1]}, {[4]}]}] = , [{[a[1] - 1]}, {[{[a[1] - 1]}, {[4]}]}] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[2](0, 0, 0, 1, 1)}, {f[4](0, 1, 0, 0, 1), f[6](0, 1, 0, 0) + [1]}] = , [{[{[-2]}, {[-1]}]}, {[0], [{[1]}, {[1]}]}] = , [-1] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[2](1, 0, 0, 1, 1), f[3](0, 2, 0, 0, 1)}, {f[4](1, 1, 0, 0, 1), f[6](1, 1, 0, 0) + [1]}] = , [{[1/2], [{[0]}, {[1]}]}, {[{[2]}, {[2]}], [{[1]}, {[{[1]}, {[4]}]}]}] = , [1] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[3](a[1] - 1, 2, 0, 0, 1), f[2](a[1], 0, 0, 1, 1)}, {f[6](a[1], 1, 0, 0) + [1], f[4](a[1], 1, 0, 0, 1)}] = , [{[{[a[1]]}, {[a[1]]}], [{[2 a[1] - 2]}, {[a[1]]}]}, { [{[1 + a[1]]}, {[1 + a[1]]}], [{[a[1]]}, {[{[a[1]]}, {[4]}]}] }] = , [a[1]] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 2} The value of the game = , [{f[2](0, 1, 0, 1, 1)}, {f[6](0, 2, 0, 0) + [1]}] = , [{[{[{[0]}, {[0]}]}, {[1/2]}]}, {[3/4]}] = , [1/2] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[3](a[1] - 1, 3, 0, 0, 1), f[2](a[1], 1, 0, 1, 1)}, {f[6](a[1], 2, 0, 0) + [1]}] = , [{ [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], [{[{[%1, %1], [%1, {[%1, {[1 + a[1]]}]}]}, {[%1, {[a[1]]}], [{[%1, {[1 + a[1]]}]}, {[a[1]]}]}]}, {[a[1]]}]}, {[{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[1 + a[1]]}]}] %1 := {[2 a[1] - 1]} = , [{[1 + a[1]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, 3 <= a[2], a[3] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{f[2](a[1], a[2] - 1, 0, 1, 1), f[3](a[1] - 1, a[2] + 1, 0, 0, 1)}, {f[6](a[1], a[2], 0, 0) + [1]}] = , [{[{[{[%2, %2], [%2, {[%2, {[1 + a[1]]}]}]}, {[%2, {[a[1]]}], [{[%2, {[1 + a[1]]}]}, {[a[1]]}]}]}, {[a[1]]}], [{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[{[{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}, {[1 + a[1]]}]}] %1 := {[2 a[1] + a[2] - 2]} %2 := {[2 a[1] + a[2] - 3]} = , [{[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}] %1 := {[2 a[1] + a[2] - 2]} For the domain, {a[5] = 1, 3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[2](0, a[2] - 1, 0, 1, 1)}, {f[6](0, a[2], 0, 0) + [1]}] = , [{[{[{[-2 + a[2]]}, {[-2 + a[2]]}], [{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}]}, {[{[-2 + a[2]]}, {[1]}], [{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]} , {[{[{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}, {[1]}]}] = , [{[{[{[-2 + a[2]]}, {[-2 + a[2]]}], [{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}]}, {[{[-2 + a[2]]}, {[1]}], [{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]} , {[1]}] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 1, 1, 0, 1), f[3](1, 0, 0, 1, 1)}, {f[6](1, 0, 1, 0) + [1], f[4](1, 0, 1, 0, 1)}] = , [{[1], [5/4]}, {[2]}] = , [3/2] For the domain, {a[5] = 1, a[3] = 1, a[1] = 2, a[2] = 0, a[4] = 0} The value of the game = , [ {f[3](2, 0, 0, 1, 1), f[3](1, 1, 1, 0, 1)}, {f[6](2, 0, 1, 0) + [1], f[4](2, 0, 1, 0, 1)}] = , [{[2], [{[3]}, {[5/2]}]}, {[3]}] = , [5/2] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 3} The value of the game = , [ {f[3](3, 0, 0, 1, 1), f[3](2, 1, 1, 0, 1)}, {f[6](3, 0, 1, 0) + [1], f[4](3, 0, 1, 0, 1)}] = , [{[3], [{[5]}, {[7/2]}]}, {[4]}] = , [7/2] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 4} The value of the game = , [ {f[3](4, 0, 0, 1, 1), f[3](3, 1, 1, 0, 1)}, {f[6](4, 0, 1, 0) + [1], f[4](4, 0, 1, 0, 1)}] = , [{[{[7]}, {[9/2]}], [4]}, {[5]}] = , [9/2] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, 5 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 1, 1, 0, 1), f[3](a[1], 0, 0, 1, 1)}, {f[4](a[1], 0, 1, 0, 1), f[6](a[1], 0, 1, 0) + [1]}] = , [{[a[1]], [{[2 a[1] - 1]}, {[{[a[1]]}, {[6]}]}]}, {[1 + a[1]]} ] = , [a[1] + 1/2] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[3](1, 0, a[3] - 1, 1, 1), f[3](0, 1, a[3], 0, 1)}, {f[4](1, 0, a[3], 0, 1), f[6](1, 0, a[3], 0) + [1]}] = , [{[{[-1 + 2 a[3]]}, {[1/2 + a[3]]}], [a[3]]}, {[a[3] + 1]}] = , [1/2 + a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 2, a[2] = 0, a[4] = 0} The value of the game = , [ {f[3](1, 1, a[3], 0, 1), f[3](2, 0, a[3] - 1, 1, 1)}, {f[4](2, 0, a[3], 0, 1), f[6](2, 0, a[3], 0) + [1]}] = , [{[a[3] + 1], [{[1 + 2 a[3]]}, {[3/2 + a[3]]}]}, {[2 + a[3]]}] = , [3/2 + a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, a[4] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 1, a[3], 0, 1), f[3](3, 0, a[3] - 1, 1, 1)}, {f[6](3, 0, a[3], 0) + [1], f[4](3, 0, a[3], 0, 1)}] = , [{[2 + a[3]], [{[3 + 2 a[3]]}, {[5/2 + a[3]]}]}, {[3 + a[3]]}] = , [5/2 + a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{ f[3](a[1] - 1, 1, a[3], 0, 1), f[3](a[1], 0, a[3] - 1, 1, 1)} , {f[6](a[1], 0, a[3], 0) + [1], f[4](a[1], 0, a[3], 0, 1)}] = , [{[a[1] + a[3] - 1], [{[2 a[1] + 2 a[3] - 3]}, {[a[1] - 1/2 + a[3]]}]}, {[a[1] + a[3]]}] = , [a[1] - 1/2 + a[3]] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 1, 0, 1, 1), f[3](1, 0, 0, 0, 2)}, {f[4](1, 0, 0, 1, 1), f[6](1, 0, 0, 1) + [1]}] = , [{[1], [{[0]}, {[1]}]}, {[3/2], [{[2]}, {[2]}]}] = , [5/4] For the domain, {a[5] = 1, a[4] = 1, a[1] = 2, a[2] = 0, a[3] = 0} The value of the game = , [ {f[3](1, 1, 0, 1, 1), f[3](2, 0, 0, 0, 2)}, {f[6](2, 0, 0, 1) + [1], f[4](2, 0, 0, 1, 1)}] = , [{[3], [{[2]}, {[2]}]}, {[5/2], [{[4]}, {[3]}]}] = , [{[3]}, {[5/2]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 1, 0, 1, 1), f[3](3, 0, 0, 0, 2)}, {f[4](3, 0, 0, 1, 1), f[6](3, 0, 0, 1) + [1]}] = , [{[5], [{[4]}, {[3]}]}, {[7/2], [{[6]}, {[4]}]}] = , [{[5]}, {[7/2]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 4} The value of the game = , [ {f[3](3, 1, 0, 1, 1), f[3](4, 0, 0, 0, 2)}, {f[4](4, 0, 0, 1, 1), f[6](4, 0, 0, 1) + [1]}] = , [{[7], [{[6]}, {[4]}]}, {[9/2], [{[8]}, {[5]}]}] = , [{[7]}, {[9/2]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, 5 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 1, 0, 1, 1), f[3](a[1], 0, 0, 0, 2)}, {f[6](a[1], 0, 0, 1) + [1], f[4](a[1], 0, 0, 1, 1)}] = , [{[2 a[1] - 1], [{[2 a[1] - 2]}, {[a[1]]}]}, {[{[2 a[1]]}, {[1 + a[1]]}], [{[a[1]]}, {[6]}]}] = , [{[2 a[1] - 1]}, {[{[a[1]]}, {[6]}]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, 1, a[3], 1, 1), f[3](a[1], 0, a[3] - 1, 2, 1), f[3](a[1], 0, a[3], 0, 2)}, {f[6](a[1], 0, a[3], 1) + [1], f[4](a[1], 0, a[3], 1, 1)}] = , [{[2 a[1] + 2 a[3] - 1], [{[2 a[1] + 2 a[3] - 2]}, {[a[1] + a[3]]}], [{[2 a[1] + 2 a[3] - 2]}, {[a[1] - 1/2 + a[3]]}]}, { [a[1] + a[3] + 1/2], [{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}]}] = , [{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, a[3] = 0, 1 <= a[1]} The value of the game = , [{ f[3](a[1] - 1, 1, 0, a[4], 1), f[3](a[1], 0, 0, a[4] - 1, 2)} , {f[6](a[1], 0, 0, a[4]) + [1], f[4](a[1], 0, 0, a[4], 1)}] = , [{[2 a[1] + a[4] - 2], [{[2 a[1] + a[4] - 3]}, {[a[1]]}]}, {[a[1] + 1/2], [{[2 a[1] - 1 + a[4]]}, {[1 + a[1]]}]}] = , [{[2 a[1] + a[4] - 2]}, {[a[1] + 1/2]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, 1, a[3], a[4], 1), f[3](a[1], 0, a[3], a[4] - 1, 2), f[3](a[1], 0, a[3] - 1, a[4] + 1, 1)}, { f[6](a[1], 0, a[3], a[4]) + [1], f[4](a[1], 0, a[3], a[4], 1) }] = , [{[2 a[1] + 2 a[3] + a[4] - 2], [{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3]]}], [{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] - 1/2 + a[3]]}]}, { [a[1] + a[3] + 1/2], [{[2 a[1] - 1 + 2 a[3] + a[4]]}, {[a[1] + 1 + a[3]]}]}] = , [{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + a[3] + 1/2]}] For the domain, {a[5] = 1, a[4] = 0, a[1] = 1, a[2] = 1, 1 <= a[3]} The value of the game = , [ {f[3](1, 1, a[3] - 1, 1, 1), f[3](0, 2, a[3], 0, 1)}, {f[4](1, 1, a[3], 0, 1), f[6](1, 1, a[3], 0) + [1]}] = , [{[{[2 a[3]]}, {[a[3] + 1]}], [a[3]]}, {[3 + a[3]], [3/2 + a[3]]}] = , [a[3] + 1] For the domain, {a[5] = 1, a[1] = 2, a[4] = 0, a[2] = 1, 1 <= a[3]} The value of the game = , [ {f[3](1, 2, a[3], 0, 1), f[3](2, 1, a[3] - 1, 1, 1)}, {f[6](2, 1, a[3], 0) + [1], f[4](2, 1, a[3], 0, 1)}] = , [{[a[3] + 1], [{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[5/2 + a[3]], [4 + a[3]]}] = , [2 + a[3]] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, a[2] = 1, a[1] = 3} The value of the game = , [ {f[3](3, 1, 0, 1, 1), f[3](2, 2, 1, 0, 1)}, {f[4](3, 1, 1, 0, 1), f[6](3, 1, 1, 0) + [1]}] = , [{[3], [{[6]}, {[4]}]}, {[9/2], [11/2]}] = , [4] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, a[2] = 1, a[1] = 3} The value of the game = , [ {f[3](2, 2, a[3], 0, 1), f[3](3, 1, a[3] - 1, 1, 1)}, {f[4](3, 1, a[3], 0, 1), f[6](3, 1, a[3], 0) + [1]}] = , [{[{[4 + 2 a[3]]}, {[3 + a[3]]}], [2 + a[3]]}, {[5 + a[3]], [7/2 + a[3]]}] = , [3 + a[3]] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 2, 1, 0, 1), f[3](a[1], 1, 0, 1, 1)}, {f[4](a[1], 1, 1, 0, 1), f[6](a[1], 1, 1, 0) + [1]}] = , [{[a[1]], [{[2 a[1]]}, {[1 + a[1]]}]}, {[{[a[1] + 2]}, {[a[1] + 2]}], [a[1] + 3/2]}] = , [1 + a[1]] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{ f[3](a[1] - 1, 2, a[3], 0, 1), f[3](a[1], 1, a[3] - 1, 1, 1)} , {f[4](a[1], 1, a[3], 0, 1), f[6](a[1], 1, a[3], 0) + [1]}] = , [{ [{[2 a[1] - 2 + 2 a[3]]}, {[a[1] + a[3]]}], [a[1] + a[3] - 1] }, {[a[1] + a[3] + 1/2], [a[1] + 2 + a[3]]}] = , [a[1] + a[3]] For the domain, {a[5] = 1, a[1] = 0, a[4] = 0, a[2] = 1, 1 <= a[3]} The value of the game = , [{f[3](0, 1, a[3] - 1, 1, 1)}, {f[4](0, 1, a[3], 0, 1), f[6](0, 1, a[3], 0) + [1]}] = , [{[{[-2 + 2 a[3]]}, {[a[3]]}]}, {[1/2 + a[3]], [2 + a[3]]}] = , [a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[3](0, 1, a[3] - 1, 1, 1)}, {f[4](0, 1, a[3], 0, 1), f[6](0, 1, a[3], 0) + [1]}] = , [{[{[-2 + 2 a[3]]}, {[a[3]]}]}, {[1/2 + a[3]], [2 + a[3]]}] = , [a[3]] For the domain, {a[5] = 1, 2 <= a[2], a[4] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, a[3], 0, 1), f[3](a[1], a[2], a[3] - 1, 1, 1)}, {f[6](a[1], a[2], a[3], 0) + [1]}] = , [{[a[1] + a[3] - 1], [{[2 a[1] + a[2] + 2 a[3] - 3]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] + 1/2]}] = , [a[1] + a[3]] For the domain, {a[5] = 1, 2 <= a[2], a[1] = 0, a[4] = 0, 1 <= a[3]} The value of the game = , [{f[3](0, a[2], a[3] - 1, 1, 1)}, {f[6](0, a[2], a[3], 0) + [1]}] = , [{[{[-3 + a[2] + 2 a[3]]}, {[a[3]]}]}, {[1/2 + a[3]]}] = , [a[3]] For the domain, {a[5] = 1, a[4] = 1, a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[2](a[1], 0, 0, 2, 1), f[3](a[1] - 1, 2, 0, 1, 1), f[3](a[1], 1, 0, 0, 2)}, {f[4](a[1], 1, 0, 1, 1), f[6](a[1], 1, 0, 1) + [1]}] = , [{[{[2 a[1] - 1]}, {[a[1]]}], [2 a[1]]}, {[1 + a[1]], [{[2 a[1] + 3]}, {[{[a[1] + 2]}, {[6]}]}]}] = , [{[2 a[1]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, 2 <= a[4], a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[2](a[1], 0, 0, a[4] + 1, 1), f[3](a[1], 1, 0, a[4] - 1, 2), f[3](a[1] - 1, 2, 0, a[4], 1)} , {f[4](a[1], 1, 0, a[4], 1), f[6](a[1], 1, 0, a[4]) + [1]}] = , [{[2 a[1] - 1 + a[4]], [{[2 a[1] + a[4] - 2]}, {[a[1]]}]}, {[1 + a[1]], [{[2 a[1] + 2 + a[4]]}, {[a[1] + 3]}]}] = , [{[2 a[1] - 1 + a[4]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[3] = 0, a[2] = 1} The value of the game = , [ {f[2](0, 0, 0, 2, 1), f[3](0, 1, 0, 0, 2)}, {f[6](0, 1, 0, 1) + [1], f[4](0, 1, 0, 1, 1)}] = , [{[0], [{[-1]}, {[-1]}]}, {[1], [{[3]}, {[{[2]}, {[6]}]}]}] = , [1/2] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[3] = 0, a[2] = 1} The value of the game = , [ {f[2](0, 0, 0, a[4] + 1, 1), f[3](0, 1, 0, a[4] - 1, 2)}, {f[4](0, 1, 0, a[4], 1), f[6](0, 1, 0, a[4]) + [1]}] = , [{[a[4] - 1], [{[-2 + a[4]]}, {[-1]}]}, {[1], [{[2 + a[4]]}, {[3]}]}] = , [{[a[4] - 1]}, {[1]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 1, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1], 1, a[3], 0, 2), f[3](a[1] - 1, 2, a[3], 1, 1), f[3](a[1], 1, a[3] - 1, 2, 1)} , {f[4](a[1], 1, a[3], 1, 1), f[6](a[1], 1, a[3], 1) + [1]}] = , [{ [{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3]]}], [2 a[1] + 2 a[3]] }, {[a[1] + 1 + a[3]], [{[2 a[1] + 3 + 2 a[3]]}, {[a[1] + 3 + a[3]]}]}] = , [{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 1, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, 2, a[3], a[4], 1), f[3](a[1], 1, a[3], a[4] - 1, 2), f[3](a[1], 1, a[3] - 1, a[4] + 1, 1)}, { f[6](a[1], 1, a[3], a[4]) + [1], f[4](a[1], 1, a[3], a[4], 1) }] = , [{[{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + a[3]]}], [2 a[1] - 1 + 2 a[3] + a[4]]}, {[a[1] + 1 + a[3]], [{[2 a[1] + 2 + 2 a[3] + a[4]]}, {[a[1] + 3 + a[3]]}]}] = , [{[2 a[1] - 1 + 2 a[3] + a[4]]}, {[a[1] + 1 + a[3]]}] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[2] = 1, 1 <= a[3]} The value of the game = , [ {f[3](0, 1, a[3], 0, 2), f[3](0, 1, a[3] - 1, 2, 1)}, {f[6](0, 1, a[3], 1) + [1], f[4](0, 1, a[3], 1, 1)}] = , [{[{[-1 + 2 a[3]]}, {[a[3]]}], [2 a[3]]}, {[a[3] + 1], [{[3 + 2 a[3]]}, {[3 + a[3]]}]}] = , [{[2 a[3]]}, {[a[3] + 1]}] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[2] = 1, 1 <= a[3]} The value of the game = , [{f[3](0, 1, a[3], a[4] - 1, 2), f[3](0, 1, a[3] - 1, a[4] + 1, 1)}, {f[6](0, 1, a[3], a[4]) + [1], f[4](0, 1, a[3], a[4], 1)}] = , [{[{[2 a[3] + a[4] - 2]}, {[a[3]]}], [-1 + 2 a[3] + a[4]]}, {[a[3] + 1], [{[2 + 2 a[3] + a[4]]}, {[3 + a[3]]}]}] = , [{[-1 + 2 a[3] + a[4]]}, {[a[3] + 1]}] For the domain, {a[5] = 1, a[3] = 0, 1 <= a[1], a[2] = 2, 1 <= a[4]} The value of the game = , [{f[3](a[1] - 1, 3, 0, a[4], 1), f[3](a[1], 2, 0, a[4] - 1, 2), f[2](a[1], 1, 0, a[4] + 1, 1)} , {f[6](a[1], 2, 0, a[4]) + [1]}] = , [{[{[2 a[1] - 1 + a[4]]}, {[a[1]]}], [2 a[1] + a[4]], [ {[{[2 a[1] + a[4]]}, {[2 a[1] + a[4]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}] = , [{[2 a[1] + a[4]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, 3 <= a[2], a[3] = 0, 1 <= a[1], 1 <= a[4]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, 0, a[4], 1), f[3](a[1], a[2], 0, a[4] - 1, 2), f[2](a[1], a[2] - 1, 0, a[4] + 1, 1)}, {f[6](a[1], a[2], 0, a[4]) + [1]}] = , [{[2 a[1] + a[2] + a[4] - 2], [{ [{[2 a[1] + a[2] + a[4] - 2]}, {[2 a[1] + a[2] + a[4] - 2]}]} , {[{[{[2 a[1] + a[2] - 2]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}], [{[2 a[1] + a[2] + a[4] - 3]}, {[a[1]]}]}, {[1 + a[1]]}] = , [{[2 a[1] + a[2] + a[4] - 2]}, {[1 + a[1]]}] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[2] = 2, 1 <= a[4]} The value of the game = , [ {f[2](0, 1, 0, a[4] + 1, 1), f[3](0, 2, 0, a[4] - 1, 2)}, {f[6](0, 2, 0, a[4]) + [1]}] = , [{[a[4]], [{[{[a[4]]}, {[a[4]]}]}, {[1/2]}]}, {[1]}] = , [{[a[4]]}, {[1]}] For the domain, {a[5] = 1, 3 <= a[2], a[1] = 0, a[3] = 0, 1 <= a[4]} The value of the game = , [{f[2](0, a[2] - 1, 0, a[4] + 1, 1), f[3](0, a[2], 0, a[4] - 1, 2)}, {f[6](0, a[2], 0, a[4]) + [1]}] = , [{[-2 + a[2] + a[4]], [ {[{[-2 + a[2] + a[4]]}, {[-2 + a[2] + a[4]]}]}, {[{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]}, {[1]}] = , [{[-2 + a[2] + a[4]]}, {[1]}] For the domain, {a[5] = 1, 2 <= a[2], 1 <= a[1], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[3](a[1] - 1, a[2] + 1, a[3], a[4], 1), f[3](a[1], a[2], a[3] - 1, a[4] + 1, 1), f[3](a[1], a[2], a[3], a[4] - 1, 2)}, {f[6](a[1], a[2], a[3], a[4]) + [1]}] = , [{[2 a[1] + a[2] + 2 a[3] + a[4] - 2], [{[2 a[1] + a[2] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3]]}]}, {[a[1] + 1 + a[3]]}] = , [{[2 a[1] + a[2] + 2 a[3] + a[4] - 2]}, {[a[1] + 1 + a[3]]}] For the domain, {a[5] = 1, 2 <= a[2], a[1] = 0, 1 <= a[3], 1 <= a[4]} The value of the game = , [{f[3](0, a[2], a[3] - 1, a[4] + 1, 1), f[3](0, a[2], a[3], a[4] - 1, 2)}, {f[6](0, a[2], a[3], a[4]) + [1]}] = , [{[{[-3 + a[2] + 2 a[3] + a[4]]}, {[a[3]]}], [-2 + a[2] + 2 a[3] + a[4]]}, {[a[3] + 1]}] = , [{[-2 + a[2] + 2 a[3] + a[4]]}, {[a[3] + 1]}] For the domain, {a[3] = 0, a[2] = 1, 1 <= a[1], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[3](a[1] - 1, 2, 0, a[4], a[5]), f[2](a[1], 0, 0, a[4] + 1, a[5]), f[3](a[1], 1, 0, a[4] - 1, a[5] + 1)}, {f[4](a[1], 1, 0, a[4], a[5])}] = , [{[2 a[1] - 1 + a[4]]}, {[2 a[1] + 3 + a[4]]}] = , [a[4] + 2 a[1]] For the domain, {a[3] = 0, a[4] = 0, a[2] = 1, 1 <= a[1], 2 <= a[5]} The value of the game = , [ {f[2](a[1], 0, 0, 1, a[5]), f[3](a[1] - 1, 2, 0, 0, a[5])}, {f[4](a[1], 1, 0, 0, a[5])}] = , [{[2 a[1] - 1]}, {[2 a[1] + 3]}] = , [2 a[1]] For the domain, {a[2] = 0, a[3] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[3](a[1], 0, 0, a[4] - 1, a[5] + 1), f[3](a[1] - 1, 1, 0, a[4], a[5])}, {f[4](a[1], 0, 0, a[4], a[5])}] = , [{[2 a[1] + a[4] - 2]}, {[a[4] + 2 a[1]]}] = , [2 a[1] - 1 + a[4]] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [ {f[3](a[1] - 1, 1, 0, 0, a[5])}, {f[4](a[1], 0, 0, 0, a[5])}] = , [{[2 a[1] - 2]}, {[2 a[1]]}] = , [2 a[1] - 1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 1, 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](0, 0, 0, a[4] + 1, a[5]), f[3](0, 1, 0, a[4] - 1, a[5] + 1)}, {f[4](0, 1, 0, a[4], a[5])}] = , [{[a[4] - 1]}, {[3 + a[4]]}] = , [a[4]] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1, 2 <= a[5]} The value of the game = , [{f[2](0, 0, 0, 1, a[5])}, {f[4](0, 1, 0, 0, a[5])}] = , [{[-1]}, {[3]}] = , [0] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[3](0, 0, 0, a[4] - 1, a[5] + 1)}, {f[4](0, 0, 0, a[4], a[5])}] = , [{[-2 + a[4]]}, {[a[4]]}] = , [a[4] - 1] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{}, {f[4](0, 0, 0, 0, a[5])}] = , [{}, {[0]}] = , [-1] For the domain, {a[2] <= 1, 0 <= a[2], 1 <= a[1], 2 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[3](a[1], a[2], a[3] - 1, a[4] + 1, a[5]), f[3](a[1], a[2], a[3], a[4] - 1, a[5] + 1), f[3](a[1] - 1, a[2] + 1, a[3], a[4], a[5])}, {f[4](a[1], a[2], a[3], a[4], a[5])}] = , [{[2 a[1] + a[2] + 2 a[3] + a[4] - 2]}, {[2 a[1] + 3 a[2] + 2 a[3] + a[4]]}] = , [2 a[1] + a[2] + 2 a[3] + a[4] - 1] For the domain, {a[2] <= 1, 0 <= a[2], a[4] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[3](a[1], a[2], a[3] - 1, 1, a[5]), f[3](a[1] - 1, a[2] + 1, a[3], 0, a[5])}, {f[4](a[1], a[2], a[3], 0, a[5])}] = , [{[2 a[1] + a[2] + 2 a[3] - 2]}, {[2 a[1] + 3 a[2] + 2 a[3]]}] = , [2 a[1] + a[2] + 2 a[3] - 1] For the domain, {a[2] <= 1, 0 <= a[2], a[1] = 0, 2 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[3](0, a[2], a[3] - 1, a[4] + 1, a[5]), f[3](0, a[2], a[3], a[4] - 1, a[5] + 1)}, {f[4](0, a[2], a[3], a[4], a[5])}] = , [{[-2 + a[2] + 2 a[3] + a[4]]}, {[3 a[2] + 2 a[3] + a[4]]}] = , [-1 + a[2] + 2 a[3] + a[4]] For the domain, {a[2] <= 1, 0 <= a[2], a[1] = 0, a[4] = 0, 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[3](0, a[2], a[3] - 1, 1, a[5])}, {f[4](0, a[2], a[3], 0, a[5])}] = , [{[-2 + a[2] + 2 a[3]]}, {[3 a[2] + 2 a[3]]}] = , [-1 + a[2] + 2 a[3]] For the domain, {2 <= a[2], a[3] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[4]} The value of the game = , [{ f[3](a[1] - 1, a[2] + 1, 0, a[4], a[5]), f[2](a[1], a[2] - 1, 0, a[4] + 1, a[5]), f[3](a[1], a[2], 0, a[4] - 1, a[5] + 1)}, {}] = , [{[2 a[1] + a[2] + a[4] - 2], [{[a[4] + 2 a[1] + a[2] - 1]}, {[a[4] + 2 a[1] + a[2] - 1]}]} , {}] = , [a[4] + 2 a[1] + a[2] - 1] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, 0, 0, a[5]), f[2](a[1], a[2] - 1, 0, 1, a[5])}, {}] = , [{[2 a[1] + a[2] - 2], [{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {}] = , [2 a[1] + a[2] - 1] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[2](0, a[2] - 1, 0, a[4] + 1, a[5]), f[3](0, a[2], 0, a[4] - 1, a[5] + 1)}, {}] = , [{[{[a[4] - 1 + a[2]]}, {[a[4] - 1 + a[2]]}], [-2 + a[2] + a[4]]}, {}] = , [a[4] - 1 + a[2]] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{f[2](0, a[2] - 1, 0, 1, a[5])}, {}] = , [{[{[a[2] - 1]}, {[a[2] - 1]}]}, {}] = , [a[2] - 1] For the domain, {2 <= a[2], 1 <= a[1], 2 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[3](a[1] - 1, a[2] + 1, a[3], a[4], a[5]), f[3](a[1], a[2], a[3] - 1, a[4] + 1, a[5]), f[3](a[1], a[2], a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[2 a[1] + a[2] + 2 a[3] + a[4] - 2]}, {}] = , [2 a[1] + a[2] + 2 a[3] + a[4] - 1] For the domain, {2 <= a[2], a[4] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[3]} The value of the game = , [{ f[3](a[1] - 1, a[2] + 1, a[3], 0, a[5]), f[3](a[1], a[2], a[3] - 1, 1, a[5])}, {}] = , [{[2 a[1] + a[2] + 2 a[3] - 2]}, {}] = , [2 a[1] + a[2] + 2 a[3] - 1] For the domain, {2 <= a[2], a[1] = 0, 2 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[3](0, a[2], a[3] - 1, a[4] + 1, a[5]), f[3](0, a[2], a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[-2 + a[2] + 2 a[3] + a[4]]}, {}] = , [-1 + a[2] + 2 a[3] + a[4]] For the domain, {2 <= a[2], a[1] = 0, a[4] = 0, 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[3](0, a[2], a[3] - 1, 1, a[5])}, {}] = , [{[-2 + a[2] + 2 a[3]]}, {}] = , [-1 + a[2] + 2 a[3]] ########## #, f[4], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{}, {f[7](0, 0, 0, 0) + [0]}] = , [{}, {[-2]}] = , [-3] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[3](0, 0, 1, 0, 0)}, {f[7](1, 0, 0, 0) + [0]}] = , [{[-1]}, {[-1]}] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 0, 1, 0, 0)}, {f[7](a[1], 0, 0, 0) + [0]}] = , [{[a[1] - 3/2]}, {[{[a[1] - 1]}, {[a[1] - 1]}]}] = , [a[1] - 1] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[4](0, 0, 1, 0, 0)}, {f[7](0, 1, 0, 0) + [0]}] = , [{[0]}, {[{[{[0]}, {[0]}]}, {[3]}]}] = , [{[0]}, {[0]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{f[4](1, 0, 1, 0, 0)}, {f[7](1, 1, 0, 0) + [0]}] = , [{[1]}, {[{[{[1]}, {[1]}]}, {[3]}]}] = , [{[1]}, {[1]}] For the domain, {a[1] = 2, a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1} The value of the game = , [{f[4](2, 0, 1, 0, 0)}, {f[7](2, 1, 0, 0) + [0]}] = , [{[2]}, {[{[{[2]}, {[2]}]}, {[3]}]}] = , [{[2]}, {[2]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1, a[1] = 3} The value of the game = , [{f[4](3, 0, 1, 0, 0)}, {f[7](3, 1, 0, 0) + [0]}] = , [{[3]}, {[{[{[3]}, {[3]}]}, {[3]}]}] = , [{[3]}, {[3]}] For the domain, {a[3] = 0, a[4] = 0, a[5] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [{f[4](a[1], 0, 1, 0, 0)}, {f[7](a[1], 1, 0, 0) + [0]}] = , [{[a[1]]}, {[{[{[a[1]]}, {[a[1]]}]}, {[3]}]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[4](0, a[2] - 1, 1, 0, 0)}, {f[7](0, a[2], 0, 0) + [0]}] = , [{[2 a[2] - 2]}, {[{[-3 + 2 a[2]]}, {[2 a[2] + 1]}]}] = , [{[2 a[2] - 2]}, {[2 a[2] - 2]}] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[4](1, a[2] - 1, 1, 0, 0)}, {f[7](1, a[2], 0, 0) + [0]}] = , [{[2 a[2] - 1]}, {[{[2 a[2] - 2]}, {[2 a[2] + 1]}]}] = , [{[2 a[2] - 1]}, {[2 a[2] - 1]}] For the domain, {a[1] = 2, 2 <= a[2], a[3] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[4](2, a[2] - 1, 1, 0, 0)}, {f[7](2, a[2], 0, 0) + [0]}] = , [{[2 a[2]]}, {[{[2 a[2] - 1]}, {[2 a[2] + 1]}]}] = , [{[2 a[2]]}, {[2 a[2]]}] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, a[5] = 0, a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, 1, 0, 0)}, {f[7](3, a[2], 0, 0) + [0]}] = , [{[2 a[2] + 1/2]}, {[{[2 a[2]]}, {[2 a[2] + 1]}]}] = , [{[2 a[2] + 1/2]}, {[2 a[2] + 1/2]}] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, a[5] = 0, 4 <= a[1]} The value of the game = , [{f[4](a[1], a[2] - 1, 1, 0, 0)}, {f[7](a[1], a[2], 0, 0) + [0]}] = , [{[{[a[1] + 2 a[2] - 3]}, {[a[1] + 2 a[2] - 3]}]}, {[{[a[1] + 2 a[2] - 3]}, {[2 a[2] + 1]}]}] = , [a[1] + 2 a[2] - 3] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[4](0, 0, 0, 1, 0)}, {f[7](0, 0, 1, 0) + [0]}] = , [{[-1]}, {[{[0]}, {[0]}]}] = , [0] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 2} The value of the game = , [{f[4](0, 0, 1, 1, 0)}, {f[7](0, 0, 2, 0) + [0]}] = , [{[{[1]}, {[1]}]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {3 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{f[4](0, 0, a[3] - 1, 1, 0)}, {f[7](0, 0, a[3], 0) + [0]}] = , [{[{[a[3] - 1]}, {[a[3] - 1]}]}, {[{[a[3] - 1]}, {[a[3] - 1]}]}] = , [a[3] - 1] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [ {f[4](0, a[2], 0, 1, 0), f[4](0, a[2] - 1, 2, 0, 0)}, {f[7](0, a[2], 1, 0) + [0]}] = , [{[2 a[2] - 1]}, {[{[2 a[2]]}, {[2 a[2]]}]}] = , [2 a[2]] For the domain, {a[1] = 0, a[4] = 0, a[5] = 0, a[3] = 2, 1 <= a[2]} The value of the game = , [ {f[4](0, a[2] - 1, 3, 0, 0), f[4](0, a[2], 1, 1, 0)}, {f[7](0, a[2], 2, 0) + [0]}] = , [{[2 a[2]], [%1, %1]}, {[%1, %1]}] %1 := {[2 a[2] + 1]} = , [2 a[2] + 1] For the domain, {3 <= a[3], a[1] = 0, a[4] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2] - 1, a[3] + 1, 0, 0), f[4](0, a[2], a[3] - 1, 1, 0)}, {f[7](0, a[2], a[3], 0) + [0]}] = , [{[%1, %1], [2 a[2] - 2 + a[3]]}, {[%1, %1]}] %1 := {[2 a[2] + a[3] - 1]} = , [2 a[2] + a[3] - 1] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 0, 2, 0, 0), f[4](1, 0, 0, 1, 0)}, {f[7](1, 0, 1, 0) + [0]}] = , [{[0]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1, a[3] = 2} The value of the game = , [ {f[3](0, 0, 3, 0, 0), f[4](1, 0, 1, 1, 0)}, {f[7](1, 0, 2, 0) + [0]}] = , [{[1], [{[2]}, {[2]}]}, {[{[2]}, {[2]}]}] = , [2] For the domain, {3 <= a[3], a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 0, a[3] + 1, 0, 0), f[4](1, 0, a[3] - 1, 1, 0)}, {f[7](1, 0, a[3], 0) + [0]}] = , [{[a[3] - 1], [{[a[3]]}, {[a[3]]}]}, {[{[a[3]]}, {[a[3]]}]}] = , [a[3]] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [ {f[4](1, a[2] - 1, 2, 0, 0), f[4](1, a[2], 0, 1, 0)}, {f[7](1, a[2], 1, 0) + [0]}] = , [{[2 a[2]]}, {[{[2 a[2] + 1]}, {[2 a[2] + 1]}]}] = , [2 a[2] + 1] For the domain, {a[4] = 0, a[5] = 0, a[1] = 1, a[3] = 2, 1 <= a[2]} The value of the game = , [ {f[4](1, a[2] - 1, 3, 0, 0), f[4](1, a[2], 1, 1, 0)}, {f[7](1, a[2], 2, 0) + [0]}] = , [{[2 a[2] + 1], [%1, %1]}, {[%1, %1]}] %1 := {[2 a[2] + 2]} = , [2 a[2] + 2] For the domain, {3 <= a[3], a[4] = 0, a[5] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2] - 1, a[3] + 1, 0, 0), f[4](1, a[2], a[3] - 1, 1, 0)}, {f[7](1, a[2], a[3], 0) + [0]}] = , [{[2 a[2] + a[3] - 1], [%1, %1]}, {[%1, %1]}] %1 := {[2 a[2] + a[3]]} = , [2 a[2] + a[3]] For the domain, {a[3] = 1, a[1] = 2, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [ {f[3](1, 0, 2, 0, 0), f[4](2, 0, 0, 1, 0)}, {f[7](2, 0, 1, 0) + [0]}] = , [{[3/2], [{[2]}, {[2]}]}, {[{[2]}, {[2]}]}] = , [2] For the domain, {a[1] = 2, a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 2} The value of the game = , [ {f[3](1, 0, 3, 0, 0), f[4](2, 0, 1, 1, 0)}, {f[7](2, 0, 2, 0) + [0]}] = , [{[5/2], [{[3]}, {[3]}]}, {[{[3]}, {[3]}]}] = , [3] For the domain, {3 <= a[3], a[1] = 2, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [ {f[3](1, 0, a[3] + 1, 0, 0), f[4](2, 0, a[3] - 1, 1, 0)}, {f[7](2, 0, a[3], 0) + [0]}] = , [{[1/2 + a[3]], [{[a[3] + 1]}, {[a[3] + 1]}]}, {[{[a[3] + 1]}, {[a[3] + 1]}]}] = , [a[3] + 1] For the domain, {a[3] = 1, a[1] = 2, a[4] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [ {f[4](2, a[2] - 1, 2, 0, 0), f[4](2, a[2], 0, 1, 0)}, {f[7](2, a[2], 1, 0) + [0]}] = , [{[2 a[2] + 1]}, {[{[2 a[2] + 2]}, {[2 a[2] + 2]}]}] = , [2 a[2] + 2] For the domain, {a[1] = 2, a[4] = 0, a[5] = 0, a[3] = 2, 1 <= a[2]} The value of the game = , [ {f[4](2, a[2] - 1, 3, 0, 0), f[4](2, a[2], 1, 1, 0)}, {f[7](2, a[2], 2, 0) + [0]}] = , [{[2 a[2] + 2], [%1, %1]}, {[%1, %1]}] %1 := {[2 a[2] + 3]} = , [2 a[2] + 3] For the domain, {3 <= a[3], a[1] = 2, a[4] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](2, a[2] - 1, a[3] + 1, 0, 0), f[4](2, a[2], a[3] - 1, 1, 0)}, {f[7](2, a[2], a[3], 0) + [0]}] = , [{[2 a[2] + a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[2 a[2] + a[3] + 1]} = , [2 a[2] + a[3] + 1] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 3} The value of the game = , [ {f[4](3, 0, 0, 1, 0), f[3](2, 0, 2, 0, 0)}, {f[7](3, 0, 1, 0) + [0]}] = , [{[{[3]}, {[3]}], [5/2]}, {[{[3]}, {[3]}]}] = , [3] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [ {f[4](3, a[2] - 1, 2, 0, 0), f[4](3, a[2], 0, 1, 0)}, {f[7](3, a[2], 1, 0) + [0]}] = , [{[2 a[2] + 2]}, {[{[2 a[2] + 5/2]}, {[2 a[2] + 5/2]}]}] = , [2 a[2] + 5/2] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 2, a[1] = 3} The value of the game = , [ {f[3](2, 0, 3, 0, 0), f[4](3, 0, 1, 1, 0)}, {f[7](3, 0, 2, 0) + [0]}] = , [{[7/2], [{[4]}, {[4]}]}, {[{[4]}, {[4]}]}] = , [4] For the domain, {3 <= a[3], a[2] = 0, a[4] = 0, a[5] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 0, a[3] + 1, 0, 0), f[4](3, 0, a[3] - 1, 1, 0)}, {f[7](3, 0, a[3], 0) + [0]}] = , [{[{[2 + a[3]]}, {[2 + a[3]]}], [3/2 + a[3]]}, {[{[2 + a[3]]}, {[2 + a[3]]}]}] = , [2 + a[3]] For the domain, {a[4] = 0, a[5] = 0, a[3] = 2, 1 <= a[2], a[1] = 3} The value of the game = , [ {f[4](3, a[2] - 1, 3, 0, 0), f[4](3, a[2], 1, 1, 0)}, {f[7](3, a[2], 2, 0) + [0]}] = , [{[2 a[2] + 3], [2 a[2] + 15/4]}, {[{[2 a[2] + 4]}, {[2 a[2] + 4]}]}] = , [2 a[2] + 4] For the domain, {3 <= a[3], a[4] = 0, a[5] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, a[3] + 1, 0, 0), f[4](3, a[2], a[3] - 1, 1, 0)}, {f[7](3, a[2], a[3], 0) + [0]}] = , [{[2 a[2] + a[3] + 1], [%1, %1]}, {[%1, %1]}] %1 := {[2 a[2] + a[3] + 2]} = , [2 a[2] + a[3] + 2] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[5] = 0, 4 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 0, 2, 0, 0), f[4](a[1], 0, 0, 1, 0)}, {f[7](a[1], 0, 1, 0) + [0]}] = , [{[a[1] - 1/2], [{[a[1]]}, {[a[1]]}]}, {[{[a[1]]}, {[a[1]]}]}] = , [a[1]] For the domain, {a[3] = 1, a[4] = 0, a[5] = 0, 1 <= a[2], 4 <= a[1]} The value of the game = , [ {f[4](a[1], a[2] - 1, 2, 0, 0), f[4](a[1], a[2], 0, 1, 0)}, {f[7](a[1], a[2], 1, 0) + [0]}] = , [{[a[1] + 2 a[2] - 1]}, {[a[1] + 2 a[2] - 1]}] For the domain, {a[2] = 0, a[4] = 0, a[5] = 0, a[3] = 2, 4 <= a[1]} The value of the game = , [ {f[4](a[1], 0, 1, 1, 0), f[3](a[1] - 1, 0, 3, 0, 0)}, {f[7](a[1], 0, 2, 0) + [0]}] = , [{[a[1] + 1/2], [{[1 + a[1]]}, {[1 + a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] = , [1 + a[1]] For the domain, {3 <= a[3], a[2] = 0, a[4] = 0, a[5] = 0, 4 <= a[1]} The value of the game = , [{f[4](a[1], 0, a[3] - 1, 1, 0), f[3](a[1] - 1, 0, a[3] + 1, 0, 0)}, {f[7](a[1], 0, a[3], 0) + [0]}] = , [{[a[1] - 3/2 + a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[a[1] + a[3] - 1]} = , [a[1] + a[3] - 1] For the domain, {a[4] = 0, a[5] = 0, a[3] = 2, 1 <= a[2], 4 <= a[1]} The value of the game = , [ {f[4](a[1], a[2] - 1, 3, 0, 0), f[4](a[1], a[2], 1, 1, 0)}, {f[7](a[1], a[2], 2, 0) + [0]}] = , [{[a[1] + 2 a[2]]}, {[{[a[1] + 2 a[2] + 1]}, {[a[1] + 2 a[2] + 1]}]}] = , [a[1] + 2 a[2] + 1] For the domain, {3 <= a[3], a[4] = 0, a[5] = 0, 1 <= a[2], 4 <= a[1]} The value of the game = , [{f[4](a[1], a[2] - 1, a[3] + 1, 0, 0), f[4](a[1], a[2], a[3] - 1, 1, 0)}, {f[7](a[1], a[2], a[3], 0) + [0]}] = , [{[%1, %1], [a[1] + 2 a[2] - 2 + a[3]]}, {[%1, %1]}] %1 := {[a[1] + 2 a[2] + a[3] - 1]} = , [a[1] + 2 a[2] + a[3] - 1] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0} The value of the game = , [{f[4](0, 0, 0, 0, 1)}, {f[7](0, 0, 0, 1) + [0]}] = , [{[-2]}, {[0]}] = , [-1] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 0, 1, 1, 0), f[4](1, 0, 0, 0, 1)}, {f[7](1, 0, 0, 1) + [0]}] = , [{[{[0]}, {[0]}]}, {[1]}] = , [0] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[5] = 0, 2 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 0, 1, 1, 0), f[4](a[1], 0, 0, 0, 1)}, {f[7](a[1], 0, 0, 1) + [0]}] = , [{[a[1]], [{[a[1] - 1/2]}, {[a[1] - 1/2]}]}, {[a[1]]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[4](0, 1, 0, 0, 1), f[4](0, 0, 1, 1, 0)}, {f[7](0, 1, 0, 1) + [0]}] = , [{[{[1]}, {[1]}]}, {[{[1]}, {[5]}]}] = , [1] For the domain, {a[4] = 1, 2 <= a[2], a[1] = 0, a[3] = 0, a[5] = 0} The value of the game = , [ {f[4](0, a[2] - 1, 1, 1, 0), f[4](0, a[2], 0, 0, 1)}, {f[7](0, a[2], 0, 1) + [0]}] = , [{[{[2 a[2] - 1]}, {[2 a[2] - 1]}]}, {[{[2 a[2] - 1]}, {[2 a[2] + 3]}]}] = , [2 a[2] - 1] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, a[1] = 1, a[2] = 1} The value of the game = , [ {f[4](1, 0, 1, 1, 0), f[4](1, 1, 0, 0, 1)}, {f[7](1, 1, 0, 1) + [0]}] = , [{[{[2]}, {[2]}]}, {[{[2]}, {[5]}]}] = , [2] For the domain, {a[4] = 1, 2 <= a[2], a[3] = 0, a[5] = 0, a[1] = 1} The value of the game = , [ {f[4](1, a[2], 0, 0, 1), f[4](1, a[2] - 1, 1, 1, 0)}, {f[7](1, a[2], 0, 1) + [0]}] = , [{[{[2 a[2]]}, {[2 a[2]]}]}, {[{[2 a[2]]}, {[2 a[2] + 3]}]}] = , [2 a[2]] For the domain, {a[4] = 1, a[1] = 2, a[3] = 0, a[5] = 0, a[2] = 1} The value of the game = , [ {f[4](2, 1, 0, 0, 1), f[4](2, 0, 1, 1, 0)}, {f[7](2, 1, 0, 1) + [0]}] = , [{[{[3]}, {[3]}]}, {[{[3]}, {[5]}]}] = , [3] For the domain, {a[4] = 1, a[1] = 2, 2 <= a[2], a[3] = 0, a[5] = 0} The value of the game = , [ {f[4](2, a[2] - 1, 1, 1, 0), f[4](2, a[2], 0, 0, 1)}, {f[7](2, a[2], 0, 1) + [0]}] = , [{[{[2 a[2] + 1]}, {[2 a[2] + 1]}]}, {[{[2 a[2] + 1]}, {[2 a[2] + 3]}]}] = , [2 a[2] + 1] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, a[2] = 1, a[1] = 3} The value of the game = , [ {f[4](3, 0, 1, 1, 0), f[4](3, 1, 0, 0, 1)}, {f[7](3, 1, 0, 1) + [0]}] = , [{[{[4]}, {[4]}]}, {[{[4]}, {[5]}]}] = , [4] For the domain, {a[4] = 1, 2 <= a[2], a[3] = 0, a[5] = 0, a[1] = 3} The value of the game = , [ {f[4](3, a[2] - 1, 1, 1, 0), f[4](3, a[2], 0, 0, 1)}, {f[7](3, a[2], 0, 1) + [0]}] = , [{[{[2 a[2] + 3/2]}, {[2 a[2] + 3/2]}], [2 a[2] + 7/4]}, {[{[2 a[2] + 2]}, {[2 a[2] + 3]}]}] = , [2 a[2] + 2] For the domain, {a[4] = 1, a[3] = 0, a[5] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [ {f[4](a[1], 1, 0, 0, 1), f[4](a[1], 0, 1, 1, 0)}, {f[7](a[1], 1, 0, 1) + [0]}] = , [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[{[1 + a[1]]}, {[5]}]}] = , [1 + a[1]] For the domain, {a[4] = 1, 2 <= a[2], a[3] = 0, a[5] = 0, 4 <= a[1]} The value of the game = , [ {f[4](a[1], a[2] - 1, 1, 1, 0), f[4](a[1], a[2], 0, 0, 1)}, {f[7](a[1], a[2], 0, 1) + [0]}] = , [{[a[1] + 2 a[2] - 2]}, {[{[a[1] + 2 a[2] - 1]}, {[2 a[2] + 3]}]}] = , [a[1] + 2 a[2] - 1] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [ {f[4](0, 0, 0, 2, 0), f[4](0, 0, 1, 0, 1)}, {f[7](0, 0, 1, 1) + [0]}] = , [{[1], [{[{[0]}, {[1]}]}, {[0]}]}, {[1]}] = , [{[1]}, {[1]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2] - 1, 2, 1, 0), f[4](0, a[2], 1, 0, 1), f[4](0, a[2], 0, 2, 0)}, {f[7](0, a[2], 1, 1) + [0]}] = , [{[{[2 a[2]]}, {[2 a[2]]}], [2 a[2] + 1], [{[{[3 a[2]]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}, {[2 a[2] + 1]} ] = , [{[2 a[2] + 1]}, {[2 a[2] + 1]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{ f[4](1, 0, 1, 0, 1), f[4](1, 0, 0, 2, 0), f[3](0, 0, 2, 1, 0) }, {f[7](1, 0, 1, 1) + [0]}] = , [{[{[1]}, {[1]}], [2], [{[{[2]}, {[2]}]}, {[1]}]}, {[2]}] = , [{[2]}, {[2]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2] - 1, 2, 1, 0), f[4](1, a[2], 0, 2, 0), f[4](1, a[2], 1, 0, 1)}, {f[7](1, a[2], 1, 1) + [0]}] = , [{[{[2 a[2] + 1]}, {[2 a[2] + 1]}], [2 a[2] + 2], [{[{[3 a[2] + 2]}, {[2 a[2] + 2]}]}, {[2 a[2] + 1]}]}, {[2 a[2] + 2]}] = , [{[2 a[2] + 2]}, {[2 a[2] + 2]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 2, a[2] = 0, a[5] = 0} The value of the game = , [{ f[3](1, 0, 2, 1, 0), f[4](2, 0, 0, 2, 0), f[4](2, 0, 1, 0, 1) }, {f[7](2, 0, 1, 1) + [0]}] = , [{[3], [{[5/2]}, {[5/2]}], [{[{[4]}, {[3]}]}, {[2]}]}, {[3]}] = , [{[3]}, {[3]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 2, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](2, a[2] - 1, 2, 1, 0), f[4](2, a[2], 0, 2, 0), f[4](2, a[2], 1, 0, 1)}, {f[7](2, a[2], 1, 1) + [0]}] = , [{[{[2 a[2] + 2]}, {[2 a[2] + 2]}], [2 a[2] + 3], [{[{[3 a[2] + 4]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]}, {[2 a[2] + 3]}] = , [{[2 a[2] + 3]}, {[2 a[2] + 3]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, a[1] = 3} The value of the game = , [{ f[3](2, 0, 2, 1, 0), f[4](3, 0, 0, 2, 0), f[4](3, 0, 1, 0, 1) }, {f[7](3, 0, 1, 1) + [0]}] = , [{[4], [{[{[6]}, {[4]}]}, {[3]}], [{[7/2]}, {[7/2]}]}, {[4]}] = , [{[4]}, {[4]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, 2, 1, 0), f[4](3, a[2], 0, 2, 0), f[4](3, a[2], 1, 0, 1)}, {f[7](3, a[2], 1, 1) + [0]}] = , [{[{[2 a[2] + 3]}, {[2 a[2] + 3]}], [2 a[2] + 7/2], [{[{[3 a[2] + 6]}, {[2 a[2] + 7/2]}]}, {[2 a[2] + 3]}]}, {[2 a[2] + 4]}] = , [2 a[2] + 15/4] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[5] = 0, 4 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 0, 2, 1, 0), f[4](a[1], 0, 0, 2, 0), f[4](a[1], 0, 1, 0, 1)}, {f[7](a[1], 0, 1, 1) + [0]}] = , [{[1 + a[1]], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], [{[a[1] + 1/2]}, {[a[1] + 1/2]}]}, {[1 + a[1]]}] = , [{[1 + a[1]]}, {[1 + a[1]]}] For the domain, {a[3] = 1, a[4] = 1, a[5] = 0, 1 <= a[2], 4 <= a[1]} The value of the game = , [{f[4](a[1], a[2] - 1, 2, 1, 0), f[4](a[1], a[2], 1, 0, 1), f[4](a[1], a[2], 0, 2, 0)}, {f[7](a[1], a[2], 1, 1) + [0]}] = , [{[{[a[1] + 2 a[2]]}, {[a[1] + 2 a[2]]}]}, {[a[1] + 2 a[2] + 1]}] = , [a[1] + 2 a[2]] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[4](1, 0, a[3] - 1, 2, 0), f[4](1, 0, a[3], 0, 1), f[3](0, 0, a[3] + 1, 1, 0)}, {f[7](1, 0, a[3], 1) + [0]}] = , [{[{[a[3]]}, {[a[3]]}], [a[3] + 1], [{[{[2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}]}, {[a[3] + 1]}] = , [{[a[3] + 1]}, {[a[3] + 1]}] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, a[1] = 1} The value of the game = , [{f[4](1, 0, a[3] - 1, 2, 0), f[4](1, 0, a[3], 0, 1), f[3](0, 0, a[3] + 1, 1, 0)}, {f[7](1, 0, a[3], 1) + [0]}] = , [{[{[a[3]]}, {[a[3]]}], [a[3] + 1], [{[{[2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}]}, {[a[3] + 1]}] = , [{[a[3] + 1]}, {[a[3] + 1]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 2, a[2] = 0, a[5] = 0} The value of the game = , [{f[4](2, 0, a[3], 0, 1), f[4](2, 0, a[3] - 1, 2, 0), f[3](1, 0, a[3] + 1, 1, 0)}, {f[7](2, 0, a[3], 1) + [0]}] = , [{[{[3/2 + a[3]]}, {[3/2 + a[3]]}], [{[{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}], [2 + a[3]]} , {[2 + a[3]]}] = , [{[2 + a[3]]}, {[2 + a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 2, a[2] = 0, a[5] = 0} The value of the game = , [{f[4](2, 0, a[3], 0, 1), f[4](2, 0, a[3] - 1, 2, 0), f[3](1, 0, a[3] + 1, 1, 0)}, {f[7](2, 0, a[3], 1) + [0]}] = , [{[{[3/2 + a[3]]}, {[3/2 + a[3]]}], [{[{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}], [2 + a[3]]} , {[2 + a[3]]}] = , [{[2 + a[3]]}, {[2 + a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, a[1] = 3} The value of the game = , [{f[3](2, 0, a[3] + 1, 1, 0), f[4](3, 0, a[3] - 1, 2, 0), f[4](3, 0, a[3], 0, 1)}, {f[7](3, 0, a[3], 1) + [0]}] = , [{[3 + a[3]], [{[5/2 + a[3]]}, {[5/2 + a[3]]}], [{[{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}]}, {[3 + a[3]]}] = , [{[3 + a[3]]}, {[3 + a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, a[1] = 3} The value of the game = , [{f[3](2, 0, a[3] + 1, 1, 0), f[4](3, 0, a[3] - 1, 2, 0), f[4](3, 0, a[3], 0, 1)}, {f[7](3, 0, a[3], 1) + [0]}] = , [{[3 + a[3]], [{[5/2 + a[3]]}, {[5/2 + a[3]]}], [{[{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}]}, {[3 + a[3]]}] = , [{[3 + a[3]]}, {[3 + a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[5] = 0, 4 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 0, a[3] + 1, 1, 0), f[4](a[1], 0, a[3] - 1, 2, 0), f[4](a[1], 0, a[3], 0, 1)}, {f[7](a[1], 0, a[3], 1) + [0]}] = , [{[{[a[1] - 1/2 + a[3]]}, {[a[1] - 1/2 + a[3]]}], [a[1] + a[3]], [{[{[2 a[1] - 2 + 2 a[3]]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}]}, {[a[1] + a[3]]}] = , [{[a[1] + a[3]]}, {[a[1] + a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [ {f[4](0, 0, a[3] - 1, 2, 0), f[4](0, 0, a[3], 0, 1)}, {f[7](0, 0, a[3], 1) + [0]}] = , [{[a[3]], [{[{[-2 + 2 a[3]]}, {[a[3]]}]}, {[a[3] - 1]}]}, {[a[3]]}] = , [{[a[3]]}, {[a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[5] = 0} The value of the game = , [ {f[4](0, 0, a[3] - 1, 2, 0), f[4](0, 0, a[3], 0, 1)}, {f[7](0, 0, a[3], 1) + [0]}] = , [{[a[3]], [{[{[-2 + 2 a[3]]}, {[a[3]]}]}, {[a[3] - 1]}]}, {[a[3]]}] = , [{[a[3]]}, {[a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2], a[3], 0, 1), f[4](0, a[2] - 1, a[3] + 1, 1, 0), f[4](0, a[2], a[3] - 1, 2, 0)}, {f[7](0, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3]], [{[2 a[2] + a[3] - 1]}, {[2 a[2] + a[3] - 1]}], [ {[{[3 a[2] + 2 a[3] - 2]}, {[2 a[2] + a[3]]}]}, {[2 a[2] + a[3] - 1]}]}, {[2 a[2] + a[3]]}] = , [{[2 a[2] + a[3]]}, {[2 a[2] + a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2], a[3], 0, 1), f[4](0, a[2] - 1, a[3] + 1, 1, 0), f[4](0, a[2], a[3] - 1, 2, 0)}, {f[7](0, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3]], [{[2 a[2] + a[3] - 1]}, {[2 a[2] + a[3] - 1]}], [ {[{[3 a[2] + 2 a[3] - 2]}, {[2 a[2] + a[3]]}]}, {[2 a[2] + a[3] - 1]}]}, {[2 a[2] + a[3]]}] = , [{[2 a[2] + a[3]]}, {[2 a[2] + a[3]]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2] - 1, a[3] + 1, 1, 0), f[4](1, a[2], a[3] - 1, 2, 0), f[4](1, a[2], a[3], 0, 1)}, {f[7](1, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3] + 1], [ {[{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3]]}], [{[2 a[2] + a[3]]}, {[2 a[2] + a[3]]}]}, {[2 a[2] + a[3] + 1]}] = , [{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 1]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2] - 1, a[3] + 1, 1, 0), f[4](1, a[2], a[3] - 1, 2, 0), f[4](1, a[2], a[3], 0, 1)}, {f[7](1, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3] + 1], [ {[{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3]]}], [{[2 a[2] + a[3]]}, {[2 a[2] + a[3]]}]}, {[2 a[2] + a[3] + 1]}] = , [{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 1]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 2, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](2, a[2] - 1, a[3] + 1, 1, 0), f[4](2, a[2], a[3] - 1, 2, 0), f[4](2, a[2], a[3], 0, 1)}, {f[7](2, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3] + 2], [ {[{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 1]}], [{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3] + 2]}] = , [{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 2]}] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 2, a[5] = 0, 1 <= a[2]} The value of the game = , [{f[4](2, a[2] - 1, a[3] + 1, 1, 0), f[4](2, a[2], a[3] - 1, 2, 0), f[4](2, a[2], a[3], 0, 1)}, {f[7](2, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3] + 2], [ {[{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 1]}], [{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3] + 2]}] = , [{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 2]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, a[3] + 1, 1, 0), f[4](3, a[2], a[3] - 1, 2, 0), f[4](3, a[2], a[3], 0, 1)}, {f[7](3, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3] + 3], [ {[{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[2 a[2] + a[3] + 2]}], [{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 3]}] = , [{[2 a[2] + a[3] + 3]}, {[2 a[2] + a[3] + 3]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, a[3] + 1, 1, 0), f[4](3, a[2], a[3] - 1, 2, 0), f[4](3, a[2], a[3], 0, 1)}, {f[7](3, a[2], a[3], 1) + [0]}] = , [{[2 a[2] + a[3] + 3], [ {[{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[2 a[2] + a[3] + 2]}], [{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 3]}] = , [{[2 a[2] + a[3] + 3]}, {[2 a[2] + a[3] + 3]}] For the domain, {a[4] = 1, 2 <= a[3], a[5] = 0, 1 <= a[2], 4 <= a[1]} The value of the game = , [{f[4](a[1], a[2] - 1, a[3] + 1, 1, 0), f[4](a[1], a[2], a[3] - 1, 2, 0), f[4](a[1], a[2], a[3], 0, 1)}, {f[7](a[1], a[2], a[3], 1) + [0]}] = , [{[a[1] + 2 a[2] + a[3]], [%1, %1], [{ [{[2 a[1] + 3 a[2] + 2 a[3] - 2]}, {[a[1] + 2 a[2] + a[3]]}]} , %1]}, {[a[1] + 2 a[2] + a[3]]}] %1 := {[a[1] + 2 a[2] + a[3] - 1]} = , [{[a[1] + 2 a[2] + a[3]]}, {[a[1] + 2 a[2] + a[3]]}] For the domain, {a[1] = 0, a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2} The value of the game = , [ {f[4](0, 0, a[3] - 1, 3, 0), f[4](0, 0, a[3], 1, 1)}, {f[7](0, 0, a[3], 2) + [0]}] = , [{[{[2 a[3]]}, {[a[3] + 1]}], [{[{[2 a[3] - 1]}, {[a[3]]}]}, {[a[3] - 1]}]}, {[a[3]]}] = , [{[{[2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2} The value of the game = , [{f[4](0, 0, 0, 1, 1)}, {f[7](0, 0, 0, 2) + [0]}] = , [{[{[0]}, {[1]}]}, {[0]}] = , [{[1/2]}, {[0]}] For the domain, {a[1] = 0, a[5] = 0, 1 <= a[2], 1 <= a[3], a[4] = 2} The value of the game = , [{f[4](0, a[2] - 1, a[3] + 1, 2, 0), f[4](0, a[2], a[3], 1, 1), f[4](0, a[2], a[3] - 1, 3, 0)}, {f[7](0, a[2], a[3], 2) + [0]}] = , [{[{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}], [ {[{[3 a[2] - 1 + 2 a[3]]}, {[2 a[2] + a[3]]}]}, {[2 a[2] + a[3] - 1]}]}, {[2 a[2] + a[3]]}] = , [{[{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3]]}] For the domain, {a[1] = 0, a[3] = 0, a[5] = 0, 1 <= a[2], a[4] = 2} The value of the game = , [ {f[4](0, a[2] - 1, 1, 2, 0), f[4](0, a[2], 0, 1, 1)}, {f[7](0, a[2], 0, 2) + [0]}] = , [{[{[3 a[2]]}, {[{[2 a[2]]}, {[2 a[2] + 4]}]}], [{[{[3 a[2] - 1]}, {[2 a[2]]}]}, {[2 a[2] - 1]}]}, {[2 a[2]]} ] = , [{[{[3 a[2]]}, {[2 a[2] + 1]}]}, {[2 a[2]]}] For the domain, {a[2] = 0, a[5] = 0, a[1] = 1, 1 <= a[3], a[4] = 2} The value of the game = , [{f[3](0, 0, a[3] + 1, 2, 0), f[4](1, 0, a[3] - 1, 3, 0), f[4](1, 0, a[3], 1, 1)}, {f[7](1, 0, a[3], 2) + [0]}] = , [{[{[2 + 2 a[3]]}, {[2 + a[3]]}], [{[{[2 a[3] + 1]}, {[a[3] + 1]}]}, {[a[3]]}]}, {[a[3] + 1]}] = , [{[{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1, a[4] = 2} The value of the game = , [ {f[4](1, 0, 0, 1, 1), f[3](0, 0, 1, 2, 0)}, {f[7](1, 0, 0, 2) + [0]}] = , [{[{[{[1]}, {[1]}]}, {[0]}], [{[2]}, {[2]}]}, {[1]}] = , [{[{[2]}, {[2]}]}, {[1]}] For the domain, {a[5] = 0, a[1] = 1, 1 <= a[2], 1 <= a[3], a[4] = 2} The value of the game = , [{f[4](1, a[2] - 1, a[3] + 1, 2, 0), f[4](1, a[2], a[3], 1, 1), f[4](1, a[2], a[3] - 1, 3, 0)}, {f[7](1, a[2], a[3], 2) + [0]}] = , [{[{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}], [ {[{[3 a[2] + 1 + 2 a[3]]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3]]}]}, {[2 a[2] + a[3] + 1]}] = , [{[{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 1]}] For the domain, {a[3] = 0, a[5] = 0, a[1] = 1, 1 <= a[2], a[4] = 2} The value of the game = , [ {f[4](1, a[2] - 1, 1, 2, 0), f[4](1, a[2], 0, 1, 1)}, {f[7](1, a[2], 0, 2) + [0]}] = , [{[{[3 a[2] + 2]}, {[{[2 a[2] + 1]}, {[2 a[2] + 4]}]}], [{[{[3 a[2] + 1]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}, {[2 a[2] + 1]}] = , [{[{[3 a[2] + 2]}, {[2 a[2] + 2]}]}, {[2 a[2] + 1]}] For the domain, {a[1] = 2, a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2} The value of the game = , [{f[4](2, 0, a[3], 1, 1), f[3](1, 0, a[3] + 1, 2, 0), f[4](2, 0, a[3] - 1, 3, 0)}, {f[7](2, 0, a[3], 2) + [0]}] = , [{[{[{[3 + 2 a[3]]}, {[5/2 + a[3]]}]}, {[3/2 + a[3]]}], [{[{[3 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}], [{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}] = , [{[{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}] For the domain, {a[1] = 2, a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2} The value of the game = , [ {f[4](2, 0, 0, 1, 1), f[3](1, 0, 1, 2, 0)}, {f[7](2, 0, 0, 2) + [0]}] = , [{[{[{[3]}, {[5/2]}]}, {[3/2]}], [{[4]}, {[3]}]}, {[2]}] = , [{[{[4]}, {[3]}]}, {[2]}] For the domain, {a[1] = 2, a[5] = 0, 1 <= a[2], 1 <= a[3], a[4] = 2} The value of the game = , [{f[4](2, a[2] - 1, a[3] + 1, 2, 0), f[4](2, a[2], a[3], 1, 1), f[4](2, a[2], a[3] - 1, 3, 0)}, {f[7](2, a[2], a[3], 2) + [0]}] = , [{[{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}], [ {[{[3 a[2] + 3 + 2 a[3]]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3] + 2]}] = , [{[{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[2 a[2] + a[3] + 2]}] For the domain, {a[1] = 2, a[3] = 0, a[5] = 0, 1 <= a[2], a[4] = 2} The value of the game = , [ {f[4](2, a[2] - 1, 1, 2, 0), f[4](2, a[2], 0, 1, 1)}, {f[7](2, a[2], 0, 2) + [0]}] = , [{[{[4 + 3 a[2]]}, {[{[2 a[2] + 2]}, {[2 a[2] + 4]}]}], [{[{[3 a[2] + 3]}, {[2 a[2] + 2]}]}, {[2 a[2] + 1]}]}, {[2 a[2] + 2]}] = , [{[{[4 + 3 a[2]]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, a[1] = 3} The value of the game = , [ {f[3](2, 0, 1, 2, 0), f[4](3, 0, 0, 1, 1)}, {f[7](3, 0, 0, 2) + [0]}] = , [{[{[{[5]}, {[7/2]}]}, {[5/2]}], [{[6]}, {[4]}]}, {[3]}] = , [{[{[6]}, {[4]}]}, {[3]}] For the domain, {a[3] = 0, a[5] = 0, 1 <= a[2], a[4] = 2, a[1] = 3} The value of the game = , [ {f[4](3, a[2] - 1, 1, 2, 0), f[4](3, a[2], 0, 1, 1)}, {f[7](3, a[2], 0, 2) + [0]}] = , [{[{[3 a[2] + 6]}, {[{[2 a[2] + 3]}, {[2 a[2] + 4]}]}], [{[{[3 a[2] + 5]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]}, {[2 a[2] + 3]}] = , [{[{[3 a[2] + 6]}, {[2 a[2] + 7/2]}]}, {[2 a[2] + 3]}] For the domain, {a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2, a[1] = 3} The value of the game = , [{f[4](3, 0, a[3] - 1, 3, 0), f[4](3, 0, a[3], 1, 1), f[3](2, 0, a[3] + 1, 2, 0)}, {f[7](3, 0, a[3], 2) + [0]}] = , [{[{[6 + 2 a[3]]}, {[4 + a[3]]}], [{[{[5 + 2 a[3]]}, {[7/2 + a[3]]}]}, {[5/2 + a[3]]}], [{[{[5 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}]}, {[3 + a[3]]}] = , [{[{[6 + 2 a[3]]}, {[4 + a[3]]}]}, {[3 + a[3]]}] For the domain, {a[5] = 0, 1 <= a[2], 1 <= a[3], a[4] = 2, a[1] = 3} The value of the game = , [{f[4](3, a[2], a[3] - 1, 3, 0), f[4](3, a[2], a[3], 1, 1), f[4](3, a[2] - 1, a[3] + 1, 2, 0)} , {f[7](3, a[2], a[3], 2) + [0]}] = , [{[{[3 a[2] + 2 a[3] + 6]}, {[2 a[2] + a[3] + 4]}], [ {[{[3 a[2] + 5 + 2 a[3]]}, {[2 a[2] + a[3] + 3]}]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 3]}] = , [{[{[3 a[2] + 2 a[3] + 6]}, {[2 a[2] + a[3] + 4]}]}, {[2 a[2] + a[3] + 3]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[4] = 2, 4 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 0, 1, 2, 0), f[4](a[1], 0, 0, 1, 1)}, {f[7](a[1], 0, 0, 2) + [0]}] = , [{[{[2 a[1]]}, {[1 + a[1]]}], [{[{[2 a[1] - 1]}, {[a[1] + 1/2]}]}, {[a[1] - 1/2]}]}, {[a[1]]}] = , [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[3] = 0, a[5] = 0, 1 <= a[2], a[4] = 2, 4 <= a[1]} The value of the game = , [ {f[4](a[1], a[2], 0, 1, 1), f[4](a[1], a[2] - 1, 1, 2, 0)}, {f[7](a[1], a[2], 0, 2) + [0]}] = , [{ [{[2 a[1] + 3 a[2]]}, {[{[a[1] + 2 a[2]]}, {[2 a[2] + 4]}]}], [{[{[2 a[1] + 3 a[2] - 1]}, {[a[1] + 2 a[2]]}]}, {[a[1] + 2 a[2] - 1]}]}, {[a[1] + 2 a[2]]}] = , [{[a[1] + 2 a[2]]}, {[a[1] + 2 a[2]]}] For the domain, {a[2] = 0, a[5] = 0, 1 <= a[3], a[4] = 2, 4 <= a[1]} The value of the game = , [{f[4](a[1], 0, a[3], 1, 1), f[3](a[1] - 1, 0, a[3] + 1, 2, 0), f[4](a[1], 0, a[3] - 1, 3, 0)}, {f[7](a[1], 0, a[3], 2) + [0]}] = , [{[{[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}], [{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}], [ {[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}]}, {[a[1] + a[3]]}] = , [{[{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]} ] For the domain, {a[5] = 0, 1 <= a[2], 1 <= a[3], a[4] = 2, 4 <= a[1]} The value of the game = , [{f[4](a[1], a[2] - 1, a[3] + 1, 2, 0), f[4](a[1], a[2], a[3] - 1, 3, 0), f[4](a[1], a[2], a[3], 1, 1)}, {f[7](a[1], a[2], a[3], 2) + [0]}] = , [{ [{[2 a[1] + 3 a[2] + 2 a[3]]}, {[a[1] + 2 a[2] + a[3] + 1]}], [{ [{[2 a[1] + 3 a[2] - 1 + 2 a[3]]}, {[a[1] + 2 a[2] + a[3]]}]} , {[a[1] + 2 a[2] + a[3] - 1]}]}, {[a[1] + 2 a[2] + a[3]]}] = , [{[{[2 a[1] + 3 a[2] + 2 a[3]]}, {[a[1] + 2 a[2] + a[3] + 1]}] }, {[a[1] + 2 a[2] + a[3]]}] For the domain, {a[2] = 0, a[5] = 0, a[1] = 1, 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[3](0, 0, a[3] + 1, a[4], 0), f[4](1, 0, a[3] - 1, a[4] + 1, 0), f[4](1, 0, a[3], a[4] - 1, 1)}, {f[7](1, 0, a[3], a[4]) + [0]}] = , [{[{[{[2 a[3] - 1 + a[4]]}, {[a[3] + 1]}]}, {[a[3]]}], [{[2 a[3] + a[4]]}, {[2 + a[3]]}]}, {[a[3] + 1]}] = , [{[{[2 a[3] + a[4]]}, {[2 + a[3]]}]}, {[a[3] + 1]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, a[1] = 1, 3 <= a[4]} The value of the game = , [ {f[4](1, 0, 0, a[4] - 1, 1), f[3](0, 0, 1, a[4], 0)}, {f[7](1, 0, 0, a[4]) + [0]}] = , [{[{[{[a[4] - 1]}, {[1]}]}, {[0]}], [{[a[4]]}, {[2]}]}, {[1]}] = , [{[{[a[4]]}, {[2]}]}, {[1]}] For the domain, {a[2] = 0, a[5] = 0, 2 <= a[1], 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[3](a[1] - 1, 0, a[3] + 1, a[4], 0), f[4](a[1], 0, a[3] - 1, a[4] + 1, 0), f[4](a[1], 0, a[3], a[4] - 1, 1)}, {f[7](a[1], 0, a[3], a[4]) + [0]}] = , [{[{[{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}], [{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + 1 + a[3]]}], [ {[{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + a[3]]}]}, {[a[1] + a[3] - 1]}]}, {[a[1] + a[3]]}] = , [{[{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]}] For the domain, {a[2] = 0, a[3] = 0, a[5] = 0, 2 <= a[1], 3 <= a[4]} The value of the game = , [{ f[3](a[1] - 1, 0, 1, a[4], 0), f[4](a[1], 0, 0, a[4] - 1, 1)} , {f[7](a[1], 0, 0, a[4]) + [0]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}], [{[{[2 a[1] + a[4] - 3]}, {[a[1] + 1/2]}]}, {[a[1] - 1/2]}]}, {[a[1]]}] = , [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[1] = 0, a[2] = 0, a[5] = 0, 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[4](0, 0, a[3] - 1, a[4] + 1, 0), f[4](0, 0, a[3], a[4] - 1, 1)}, {f[7](0, 0, a[3], a[4]) + [0]}] = , [{[{[{[2 a[3] + a[4] - 3]}, {[a[3]]}]}, {[a[3] - 1]}], [{[2 a[3] + a[4] - 2]}, {[a[3] + 1]}]}, {[a[3]]}] = , [{[{[2 a[3] + a[4] - 2]}, {[a[3] + 1]}]}, {[a[3]]}] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[5] = 0, 3 <= a[4]} The value of the game = , [{f[4](0, 0, 0, a[4] - 1, 1)}, {f[7](0, 0, 0, a[4]) + [0]}] = , [{[{[-2 + a[4]]}, {[1]}]}, {[0]}] For the domain, {a[5] = 0, 0 <= a[1], 1 <= a[2], 1 <= a[3], 3 <= a[4]} The value of the game = , [{ f[4](a[1], a[2] - 1, a[3] + 1, a[4], 0), f[4](a[1], a[2], a[3] - 1, a[4] + 1, 0), f[4](a[1], a[2], a[3], a[4] - 1, 1)}, {f[7](a[1], a[2], a[3], a[4]) + [0]}] = , [{[{[{[2 a[1] + 3 a[2] - 3 + 2 a[3] + a[4]]}, {[a[1] + 2 a[2] + a[3]]}]}, {[a[1] + 2 a[2] + a[3] - 1]}], [ {[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 2]}, {[a[1] + 2 a[2] + a[3] + 1]}]}, {[a[1] + 2 a[2] + a[3]]}] = , [{[{[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 2]}, {[a[1] + 2 a[2] + a[3] + 1]}]}, {[a[1] + 2 a[2] + a[3]]}] For the domain, {a[3] = 0, a[5] = 0, 0 <= a[1], 1 <= a[2], 3 <= a[4]} The value of the game = , [{f[4](a[1], a[2] - 1, 1, a[4], 0), f[4](a[1], a[2], 0, a[4] - 1, 1)}, {f[7](a[1], a[2], 0, a[4]) + [0]}] = , [{[{[{[2 a[1] + 3 a[2] - 3 + a[4]]}, {[a[1] + 2 a[2]]}]}, {[a[1] + 2 a[2] - 1]}], [{[2 a[1] + 3 a[2] - 2 + a[4]]}, {[a[1] + 2 a[2] + 1]}]}, {[a[1] + 2 a[2]]}] = , [{[{[2 a[1] + 3 a[2] - 2 + a[4]]}, {[a[1] + 2 a[2] + 1]}]}, {[a[1] + 2 a[2]]}] For the domain, {a[5] = 1, a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{}, {f[7](0, 0, 0, 0) + [1]}] = , [{}, {[-1]}] = , [-2] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[3](0, 0, 1, 0, 1)}, {f[7](1, 0, 0, 0) + [1]}] = , [{[0]}, {[0]}] For the domain, {a[5] = 1, a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 0, 1, 0, 1)}, {f[7](a[1], 0, 0, 0) + [1]}] = , [{[a[1] - 1/2]}, {[{[a[1]]}, {[a[1]]}]}] = , [a[1]] For the domain, {a[5] = 1, a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[4](0, 0, 1, 0, 1)}, {f[7](0, 1, 0, 0) + [1]}] = , [{[1]}, {[{[{[1]}, {[1]}]}, {[4]}]}] = , [{[1]}, {[1]}] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{f[4](1, 0, 1, 0, 1)}, {f[7](1, 1, 0, 0) + [1]}] = , [{[2]}, {[{[{[2]}, {[2]}]}, {[4]}]}] = , [{[2]}, {[2]}] For the domain, {a[5] = 1, a[1] = 2, a[3] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[4](2, 0, 1, 0, 1)}, {f[7](2, 1, 0, 0) + [1]}] = , [{[3]}, {[{[{[3]}, {[3]}]}, {[4]}]}] = , [{[3]}, {[3]}] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, a[2] = 1, a[1] = 3} The value of the game = , [{f[4](3, 0, 1, 0, 1)}, {f[7](3, 1, 0, 0) + [1]}] = , [{[4]}, {[{[{[4]}, {[4]}]}, {[4]}]}] = , [{[4]}, {[4]}] For the domain, {a[5] = 1, a[3] = 0, a[4] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [{f[4](a[1], 0, 1, 0, 1)}, {f[7](a[1], 1, 0, 0) + [1]}] = , [{[1 + a[1]]}, {[{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[4]}]}] = , [{[1 + a[1]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, 2 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[4](0, a[2] - 1, 1, 0, 1)}, {f[7](0, a[2], 0, 0) + [1]}] = , [{[2 a[2] - 1]}, {[{[2 a[2] - 2]}, {[2 a[2] + 2]}]}] = , [{[2 a[2] - 1]}, {[2 a[2] - 1]}] For the domain, {a[5] = 1, 2 <= a[2], a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[4](1, a[2] - 1, 1, 0, 1)}, {f[7](1, a[2], 0, 0) + [1]}] = , [{[2 a[2]]}, {[{[2 a[2] - 1]}, {[2 a[2] + 2]}]}] = , [{[2 a[2]]}, {[2 a[2]]}] For the domain, {a[5] = 1, a[1] = 2, 2 <= a[2], a[3] = 0, a[4] = 0} The value of the game = , [{f[4](2, a[2] - 1, 1, 0, 1)}, {f[7](2, a[2], 0, 0) + [1]}] = , [{[2 a[2] + 1]}, {[{[2 a[2]]}, {[2 a[2] + 2]}]}] = , [{[2 a[2] + 1]}, {[2 a[2] + 1]}] For the domain, {a[5] = 1, 2 <= a[2], a[3] = 0, a[4] = 0, a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, 1, 0, 1)}, {f[7](3, a[2], 0, 0) + [1]}] = , [{[2 a[2] + 3/2]}, {[{[2 a[2] + 1]}, {[2 a[2] + 2]}]}] = , [{[2 a[2] + 3/2]}, {[2 a[2] + 3/2]}] For the domain, {a[5] = 1, 2 <= a[2], a[3] = 0, a[4] = 0, 4 <= a[1]} The value of the game = , [{f[4](a[1], a[2] - 1, 1, 0, 1)}, {f[7](a[1], a[2], 0, 0) + [1]}] = , [{[{[a[1] + 2 a[2] - 2]}, {[a[1] + 2 a[2] - 2]}]}, {[{[a[1] + 2 a[2] - 2]}, {[2 a[2] + 2]}]}] = , [a[1] + 2 a[2] - 2] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[4](0, 0, 0, 1, 1)}, {f[7](0, 0, 1, 0) + [1]}] = , [{[{[0]}, {[1]}]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[4](0, 0, a[3] - 1, 1, 1)}, {f[7](0, 0, a[3], 0) + [1]}] = , [{[{[-2 + 2 a[3]]}, {[a[3]]}]}, {[{[a[3]]}, {[a[3]]}]}] = , [a[3]] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [ {f[4](0, a[2] - 1, 2, 0, 1), f[4](0, a[2], 0, 1, 1)}, {f[7](0, a[2], 1, 0) + [1]}] = , [{[2 a[2]], [{[3 a[2]]}, {[{[2 a[2]]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 1]}, {[2 a[2] + 1]}]}] = , [2 a[2] + 1] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2], a[3] - 1, 1, 1), f[4](0, a[2] - 1, a[3] + 1, 0, 1)}, {f[7](0, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] - 1], [{[-2 + 3 a[2] + 2 a[3]]}, {[2 a[2] + a[3]]}]}, {[{[2 a[2] + a[3]]}, {[2 a[2] + a[3]]}]}] = , [2 a[2] + a[3]] For the domain, {a[5] = 1, a[3] = 1, a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [ {f[4](0, a[2] - 1, 2, 0, 1), f[4](0, a[2], 0, 1, 1)}, {f[7](0, a[2], 1, 0) + [1]}] = , [{[2 a[2]], [{[3 a[2]]}, {[{[2 a[2]]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 1]}, {[2 a[2] + 1]}]}] = , [2 a[2] + 1] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2], a[3] - 1, 1, 1), f[4](0, a[2] - 1, a[3] + 1, 0, 1)}, {f[7](0, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] - 1], [{[-2 + 3 a[2] + 2 a[3]]}, {[2 a[2] + a[3]]}]}, {[{[2 a[2] + a[3]]}, {[2 a[2] + a[3]]}]}] = , [2 a[2] + a[3]] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 0, 2, 0, 1), f[4](1, 0, 0, 1, 1)}, {f[7](1, 0, 1, 0) + [1]}] = , [{[1], [{[2]}, {[2]}]}, {[{[2]}, {[2]}]}] = , [2] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 0, a[3] + 1, 0, 1), f[4](1, 0, a[3] - 1, 1, 1)}, {f[7](1, 0, a[3], 0) + [1]}] = , [{[{[2 a[3]]}, {[a[3] + 1]}], [a[3]]}, {[{[a[3] + 1]}, {[a[3] + 1]}]}] = , [a[3] + 1] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [ {f[4](1, a[2], 0, 1, 1), f[4](1, a[2] - 1, 2, 0, 1)}, {f[7](1, a[2], 1, 0) + [1]}] = , [{[2 a[2] + 1], [{[2 + 3 a[2]]}, {[{[2 a[2] + 1]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 2]}, {[2 a[2] + 2]}]}] = , [2 a[2] + 2] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2], a[3] - 1, 1, 1), f[4](1, a[2] - 1, a[3] + 1, 0, 1)}, {f[7](1, a[2], a[3], 0) + [1]}] = , [{ [2 a[2] + a[3]], [{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}] }, {[{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 1]}]}] = , [2 a[2] + a[3] + 1] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [ {f[4](1, a[2], 0, 1, 1), f[4](1, a[2] - 1, 2, 0, 1)}, {f[7](1, a[2], 1, 0) + [1]}] = , [{[2 a[2] + 1], [{[2 + 3 a[2]]}, {[{[2 a[2] + 1]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 2]}, {[2 a[2] + 2]}]}] = , [2 a[2] + 2] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2], a[3] - 1, 1, 1), f[4](1, a[2] - 1, a[3] + 1, 0, 1)}, {f[7](1, a[2], a[3], 0) + [1]}] = , [{ [2 a[2] + a[3]], [{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}] }, {[{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 1]}]}] = , [2 a[2] + a[3] + 1] For the domain, {a[5] = 1, a[3] = 1, a[1] = 2, a[2] = 0, a[4] = 0} The value of the game = , [ {f[3](1, 0, 2, 0, 1), f[4](2, 0, 0, 1, 1)}, {f[7](2, 0, 1, 0) + [1]}] = , [{[5/2], [{[4]}, {[3]}]}, {[{[3]}, {[3]}]}] = , [3] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 2, a[2] = 0, a[4] = 0} The value of the game = , [ {f[3](1, 0, a[3] + 1, 0, 1), f[4](2, 0, a[3] - 1, 1, 1)}, {f[7](2, 0, a[3], 0) + [1]}] = , [{[3/2 + a[3]], [{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[{[2 + a[3]]}, {[2 + a[3]]}]}] = , [2 + a[3]] For the domain, {a[5] = 1, a[3] = 1, a[1] = 2, a[4] = 0, 1 <= a[2]} The value of the game = , [ {f[4](2, a[2], 0, 1, 1), f[4](2, a[2] - 1, 2, 0, 1)}, {f[7](2, a[2], 1, 0) + [1]}] = , [{[2 a[2] + 2], [{[4 + 3 a[2]]}, {[{[2 a[2] + 2]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 3]}, {[2 a[2] + 3]}]}] = , [2 a[2] + 3] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 2, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[4](2, a[2] - 1, a[3] + 1, 0, 1), f[4](2, a[2], a[3] - 1, 1, 1)}, {f[7](2, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] + 1], [{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}] = , [2 a[2] + a[3] + 2] For the domain, {a[5] = 1, a[3] = 1, a[1] = 2, a[4] = 0, 1 <= a[2]} The value of the game = , [ {f[4](2, a[2] - 1, 2, 0, 1), f[4](2, a[2], 0, 1, 1)}, {f[7](2, a[2], 1, 0) + [1]}] = , [{[2 a[2] + 2], [{[4 + 3 a[2]]}, {[{[2 a[2] + 2]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 3]}, {[2 a[2] + 3]}]}] = , [2 a[2] + 3] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 2, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[4](2, a[2] - 1, a[3] + 1, 0, 1), f[4](2, a[2], a[3] - 1, 1, 1)}, {f[7](2, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] + 1], [{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}] = , [2 a[2] + a[3] + 2] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 0, 2, 0, 1), f[4](3, 0, 0, 1, 1)}, {f[7](3, 0, 1, 0) + [1]}] = , [{[7/2], [{[6]}, {[4]}]}, {[{[4]}, {[4]}]}] = , [4] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [ {f[4](3, a[2] - 1, 2, 0, 1), f[4](3, a[2], 0, 1, 1)}, {f[7](3, a[2], 1, 0) + [1]}] = , [{[2 a[2] + 3], [{[3 a[2] + 6]}, {[{[2 a[2] + 3]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 7/2]}, {[2 a[2] + 7/2]}]}] = , [2 a[2] + 7/2] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [ {f[4](3, a[2] - 1, 2, 0, 1), f[4](3, a[2], 0, 1, 1)}, {f[7](3, a[2], 1, 0) + [1]}] = , [{[2 a[2] + 3], [{[3 a[2] + 6]}, {[{[2 a[2] + 3]}, {[2 a[2] + 4]}]}]}, {[{[2 a[2] + 7/2]}, {[2 a[2] + 7/2]}]}] = , [2 a[2] + 7/2] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, a[4] = 0, a[1] = 3} The value of the game = , [ {f[3](2, 0, a[3] + 1, 0, 1), f[4](3, 0, a[3] - 1, 1, 1)}, {f[7](3, 0, a[3], 0) + [1]}] = , [{[5/2 + a[3]], [{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[{[3 + a[3]]}, {[3 + a[3]]}]}] = , [3 + a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, a[3] + 1, 0, 1), f[4](3, a[2], a[3] - 1, 1, 1)}, {f[7](3, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] + 2], [{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[{[2 a[2] + a[3] + 3]}, {[2 a[2] + a[3] + 3]}]}] = , [2 a[2] + a[3] + 3] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2] - 1, a[3] + 1, 0, 1), f[4](3, a[2], a[3] - 1, 1, 1)}, {f[7](3, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] + 2], [{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[{[2 a[2] + a[3] + 3]}, {[2 a[2] + a[3] + 3]}]}] = , [2 a[2] + a[3] + 3] For the domain, {a[5] = 1, a[3] = 1, a[2] = 0, a[4] = 0, 4 <= a[1]} The value of the game = , [ {f[3](a[1] - 1, 0, 2, 0, 1), f[4](a[1], 0, 0, 1, 1)}, {f[7](a[1], 0, 1, 0) + [1]}] = , [{[a[1] + 1/2], [{[2 a[1]]}, {[1 + a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}] = , [1 + a[1]] For the domain, {a[5] = 1, a[3] = 1, a[4] = 0, 1 <= a[2], 4 <= a[1]} The value of the game = , [ {f[4](a[1], a[2] - 1, 2, 0, 1), f[4](a[1], a[2], 0, 1, 1)}, {f[7](a[1], a[2], 1, 0) + [1]}] = , [{[a[1] + 2 a[2]], [{[2 a[1] + 3 a[2]]}, {[{[a[1] + 2 a[2]]}, {[2 a[2] + 4]}]}]} , {[a[1] + 2 a[2]]}] = , [{[a[1] + 2 a[2]]}, {[a[1] + 2 a[2]]}] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 0, a[3] + 1, 0, 1), f[4](1, 0, a[3] - 1, 1, 1)}, {f[7](1, 0, a[3], 0) + [1]}] = , [{[a[3]], [{[2 a[3]]}, {[a[3] + 1]}]}, {[{[a[3] + 1]}, {[a[3] + 1]}]}] = , [a[3] + 1] For the domain, {a[5] = 1, 2 <= a[3], a[2] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [{f[3](a[1] - 1, 0, a[3] + 1, 0, 1), f[4](a[1], 0, a[3] - 1, 1, 1)}, {f[7](a[1], 0, a[3], 0) + [1]}] = , [{[a[1] - 1/2 + a[3]], [{[2 a[1] - 2 + 2 a[3]]}, {[a[1] + a[3]]}]}, {[{[a[1] + a[3]]}, {[a[1] + a[3]]}]}] = , [a[1] + a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[4](0, 0, a[3] - 1, 1, 1)}, {f[7](0, 0, a[3], 0) + [1]}] = , [{[{[-2 + 2 a[3]]}, {[a[3]]}]}, {[{[a[3]]}, {[a[3]]}]}] = , [a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2] - 1, a[3] + 1, 0, 1), f[4](0, a[2], a[3] - 1, 1, 1)}, {f[7](0, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] - 1], [{[-2 + 3 a[2] + 2 a[3]]}, {[2 a[2] + a[3]]}]}, {[{[2 a[2] + a[3]]}, {[2 a[2] + a[3]]}]}] = , [2 a[2] + a[3]] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2] - 1, a[3] + 1, 0, 1), f[4](1, a[2], a[3] - 1, 1, 1)}, {f[7](1, a[2], a[3], 0) + [1]}] = , [{ [2 a[2] + a[3]], [{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}] }, {[{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 1]}]}] = , [2 a[2] + a[3] + 1] For the domain, {a[5] = 1, 2 <= a[3], a[1] = 2, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[4](2, a[2] - 1, a[3] + 1, 0, 1), f[4](2, a[2], a[3] - 1, 1, 1)}, {f[7](2, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] + 1], [{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}] = , [2 a[2] + a[3] + 2] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2], a[3] - 1, 1, 1), f[4](3, a[2] - 1, a[3] + 1, 0, 1)}, {f[7](3, a[2], a[3], 0) + [1]}] = , [{[2 a[2] + a[3] + 2], [{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[{[2 a[2] + a[3] + 3]}, {[2 a[2] + a[3] + 3]}]}] = , [2 a[2] + a[3] + 3] For the domain, {a[5] = 1, 2 <= a[3], a[4] = 0, 0 <= a[1], 1 <= a[2]} The value of the game = , [{f[4](a[1], a[2] - 1, a[3] + 1, 0, 1), f[4](a[1], a[2], a[3] - 1, 1, 1)}, {f[7](a[1], a[2], a[3], 0) + [1]}] = , [{[a[1] + 2 a[2] + a[3] - 1], [{[2 a[1] + 3 a[2] + 2 a[3] - 2]}, {[a[1] + 2 a[2] + a[3]]}]} , {[{[a[1] + 2 a[2] + a[3]]}, {[a[1] + 2 a[2] + a[3]]}]}] = , [a[1] + 2 a[2] + a[3]] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[4](1, 0, 0, 0, 2), f[3](0, 0, 1, 1, 1)}, {f[7](1, 0, 0, 1) + [1]}] = , [{[{[1]}, {[1]}], [2]}, {[2]}] = , [{[2]}, {[2]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[3] = 0, 2 <= a[1]} The value of the game = , [ {f[4](a[1], 0, 0, 0, 2), f[3](a[1] - 1, 0, 1, 1, 1)}, {f[7](a[1], 0, 0, 1) + [1]}] = , [{[2 a[1]], [{[2 a[1] - 1]}, {[a[1] + 1/2]}]}, {[1 + a[1]]}] = , [{[2 a[1]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{f[4](0, 0, 0, 0, 2)}, {f[7](0, 0, 0, 1) + [1]}] = , [{[0]}, {[1]}] = , [1/2] For the domain, {a[5] = 1, a[4] = 1, a[3] = 0, 0 <= a[1], 1 <= a[2]} The value of the game = , [ {f[4](a[1], a[2] - 1, 1, 1, 1), f[4](a[1], a[2], 0, 0, 2)}, {f[7](a[1], a[2], 0, 1) + [1]}] = , [{[2 a[1] + 3 a[2]], [{[2 a[1] + 3 a[2] - 1]}, {[a[1] + 2 a[2]]}]}, {[{[a[1] + 2 a[2]]}, {[2 a[2] + 4]}]}] = , [{[2 a[1] + 3 a[2]]}, {[{[a[1] + 2 a[2]]}, {[2 a[2] + 4]}]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, a[1] = 1, 1 <= a[3]} The value of the game = , [{f[4](1, 0, a[3] - 1, 2, 1), f[4](1, 0, a[3], 0, 2), f[3](0, 0, a[3] + 1, 1, 1)}, {f[7](1, 0, a[3], 1) + [1]}] = , [{[{[2 a[3] + 1]}, {[a[3] + 1]}], [2 + 2 a[3]]}, {[2 + a[3]]}] = , [{[2 + 2 a[3]]}, {[2 + a[3]]}] For the domain, {a[5] = 1, a[4] = 1, a[2] = 0, 2 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, 0, a[3] + 1, 1, 1), f[4](a[1], 0, a[3] - 1, 2, 1), f[4](a[1], 0, a[3], 0, 2)}, {f[7](a[1], 0, a[3], 1) + [1]}] = , [{[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}], [{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3]]}], [2 a[1] + 2 a[3]] }, {[a[1] + 1 + a[3]]}] = , [{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}] For the domain, {a[5] = 1, a[4] = 1, a[1] = 0, a[2] = 0, 1 <= a[3]} The value of the game = , [ {f[4](0, 0, a[3] - 1, 2, 1), f[4](0, 0, a[3], 0, 2)}, {f[7](0, 0, a[3], 1) + [1]}] = , [{[{[-1 + 2 a[3]]}, {[a[3]]}], [2 a[3]]}, {[a[3] + 1]}] = , [{[2 a[3]]}, {[a[3] + 1]}] For the domain, {a[5] = 1, a[4] = 1, 0 <= a[1], 1 <= a[2], 1 <= a[3]} The value of the game = , [{f[4](a[1], a[2] - 1, a[3] + 1, 1, 1), f[4](a[1], a[2], a[3], 0, 2), f[4](a[1], a[2], a[3] - 1, 2, 1)}, {f[7](a[1], a[2], a[3], 1) + [1]}] = , [{[2 a[1] + 3 a[2] + 2 a[3]], [{[2 a[1] + 3 a[2] - 1 + 2 a[3]]}, {[a[1] + 2 a[2] + a[3]]}]} , {[a[1] + 2 a[2] + a[3] + 1]}] = , [{[2 a[1] + 3 a[2] + 2 a[3]]}, {[a[1] + 2 a[2] + a[3] + 1]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, a[1] = 1, 1 <= a[3]} The value of the game = , [{f[4](1, 0, a[3] - 1, a[4] + 1, 1), f[4](1, 0, a[3], a[4] - 1, 2), f[3](0, 0, a[3] + 1, a[4], 1)} , {f[7](1, 0, a[3], a[4]) + [1]}] = , [{[{[2 a[3] + a[4]]}, {[a[3] + 1]}], [1 + 2 a[3] + a[4]]}, {[2 + a[3]]}] = , [{[1 + 2 a[3] + a[4]]}, {[2 + a[3]]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[3](0, 0, 1, a[4], 1), f[4](1, 0, 0, a[4] - 1, 2)}, {f[7](1, 0, 0, a[4]) + [1]}] = , [{[{[a[4]]}, {[1]}], [a[4] + 1]}, {[2]}] = , [{[a[4] + 1]}, {[2]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, 2 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, 0, a[3] + 1, a[4], 1), f[4](a[1], 0, a[3] - 1, a[4] + 1, 1), f[4](a[1], 0, a[3], a[4] - 1, 2)}, {f[7](a[1], 0, a[3], a[4]) + [1]}] = , [{[{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + a[3] + 1/2]}], [2 a[1] - 1 + 2 a[3] + a[4]], [{[2 a[1] + 2 a[3] + a[4] - 2]}, {[a[1] + a[3]]}]}, {[a[1] + 1 + a[3]]}] = , [{[2 a[1] - 1 + 2 a[3] + a[4]]}, {[a[1] + 1 + a[3]]}] For the domain, {a[5] = 1, 2 <= a[4], a[2] = 0, a[3] = 0, 2 <= a[1]} The value of the game = , [{ f[3](a[1] - 1, 0, 1, a[4], 1), f[4](a[1], 0, 0, a[4] - 1, 2)} , {f[7](a[1], 0, 0, a[4]) + [1]}] = , [{[2 a[1] - 1 + a[4]], [{[2 a[1] + a[4] - 2]}, {[a[1] + 1/2]}] }, {[1 + a[1]]}] = , [{[2 a[1] - 1 + a[4]]}, {[1 + a[1]]}] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[2] = 0, 1 <= a[3]} The value of the game = , [{f[4](0, 0, a[3], a[4] - 1, 2), f[4](0, 0, a[3] - 1, a[4] + 1, 1)}, {f[7](0, 0, a[3], a[4]) + [1]}] = , [{[-1 + 2 a[3] + a[4]], [{[2 a[3] + a[4] - 2]}, {[a[3]]}]}, {[a[3] + 1]}] = , [{[-1 + 2 a[3] + a[4]]}, {[a[3] + 1]}] For the domain, {a[5] = 1, 2 <= a[4], a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{f[4](0, 0, 0, a[4] - 1, 2)}, {f[7](0, 0, 0, a[4]) + [1]}] = , [{[a[4] - 1]}, {[1]}] For the domain, {a[5] = 1, 2 <= a[4], 0 <= a[1], 1 <= a[2], 1 <= a[3]} The value of the game = , [{ f[4](a[1], a[2] - 1, a[3] + 1, a[4], 1), f[4](a[1], a[2], a[3], a[4] - 1, 2), f[4](a[1], a[2], a[3] - 1, a[4] + 1, 1)}, {f[7](a[1], a[2], a[3], a[4]) + [1]}] = , [{[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 1], [ {[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 2]}, {[a[1] + 2 a[2] + a[3]]}]}, {[a[1] + 2 a[2] + a[3] + 1]}] = , [{[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}, {[a[1] + 2 a[2] + a[3] + 1]}] For the domain, {a[5] = 1, 2 <= a[4], a[3] = 0, 0 <= a[1], 1 <= a[2]} The value of the game = , [{f[4](a[1], a[2] - 1, 1, a[4], 1), f[4](a[1], a[2], 0, a[4] - 1, 2)}, {f[7](a[1], a[2], 0, a[4]) + [1]}] = , [{[2 a[1] + 3 a[2] - 1 + a[4]], [{[2 a[1] + 3 a[2] - 2 + a[4]]}, {[a[1] + 2 a[2]]}]}, {[a[1] + 2 a[2] + 1]}] = , [{[2 a[1] + 3 a[2] - 1 + a[4]]}, {[a[1] + 2 a[2] + 1]}] For the domain, {a[2] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[3](a[1] - 1, 0, a[3] + 1, a[4], a[5]), f[4](a[1], 0, a[3] - 1, a[4] + 1, a[5]), f[4](a[1], 0, a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[2 a[1] - 1 + 2 a[3] + a[4]]}, {}] = , [2 a[1] + 2 a[3] + a[4]] For the domain, {a[2] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, 0, a[3] + 1, 0, a[5]), f[4](a[1], 0, a[3] - 1, 1, a[5])}, {}] = , [{[2 a[1] + 2 a[3] - 1]}, {}] = , [2 a[1] + 2 a[3]] For the domain, {a[2] = 0, a[3] = 0, 1 <= a[1], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[3](a[1] - 1, 0, 1, a[4], a[5]), f[4](a[1], 0, 0, a[4] - 1, a[5] + 1)}, {}] = , [{[2 a[1] - 1 + a[4]]}, {}] = , [2 a[1] + a[4]] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, 1 <= a[1], 2 <= a[5]} The value of the game = , [{f[3](a[1] - 1, 0, 1, 0, a[5])}, {}] = , [{[2 a[1] - 1]}, {}] = , [2 a[1]] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{f[4](0, 0, a[3], a[4] - 1, a[5] + 1), f[4](0, 0, a[3] - 1, a[4] + 1, a[5])}, {}] = , [{[-1 + 2 a[3] + a[4]]}, {}] = , [2 a[3] + a[4]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, 2 <= a[5], 1 <= a[3]} The value of the game = , [{f[4](0, 0, a[3] - 1, 1, a[5])}, {}] = , [{[-1 + 2 a[3]]}, {}] = , [2 a[3]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[4](0, 0, 0, a[4] - 1, a[5] + 1)}, {}] = , [{[a[4] - 1]}, {}] = , [a[4]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[5]} The value of the game = , [{}, {}] = , [{}, {}] = , [0] For the domain, {0 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[4](a[1], a[2] - 1, a[3] + 1, a[4], a[5]), f[4](a[1], a[2], a[3] - 1, a[4] + 1, a[5]), f[4](a[1], a[2], a[3], a[4] - 1, a[5] + 1)}, {}] = , [{[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}, {}] = , [2 a[1] + 3 a[2] + 2 a[3] + a[4]] For the domain, {a[4] = 0, 0 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[3]} The value of the game = , [{ f[4](a[1], a[2] - 1, a[3] + 1, 0, a[5]), f[4](a[1], a[2], a[3] - 1, 1, a[5])}, {}] = , [{[2 a[1] + 3 a[2] + 2 a[3] - 1]}, {}] = , [2 a[1] + 3 a[2] + 2 a[3]] For the domain, {a[3] = 0, 0 <= a[1], 1 <= a[2], 2 <= a[5], 1 <= a[4]} The value of the game = , [{f[4](a[1], a[2] - 1, 1, a[4], a[5]), f[4](a[1], a[2], 0, a[4] - 1, a[5] + 1)}, {}] = , [{[2 a[1] + 3 a[2] - 1 + a[4]]}, {}] = , [2 a[1] + 3 a[2] + a[4]] For the domain, {a[3] = 0, a[4] = 0, 0 <= a[1], 1 <= a[2], 2 <= a[5]} The value of the game = , [{f[4](a[1], a[2] - 1, 1, 0, a[5])}, {}] = , [{[2 a[1] + 3 a[2] - 1]}, {}] = , [2 a[1] + 3 a[2]] ########## #, f[5], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{}, {f[6](0, 0, 0, 0)}] = , [{}, {[-3]}] = , [-4] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[5](0, 1, 0, 0)}, {f[6](1, 0, 0, 0)}] = , [{[{[-1]}, {[-1]}]}, {[{[-1]}, {[-1]}]}] = , [-1] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [{f[5](a[1] - 1, 1, 0, 0)}, {f[6](a[1], 0, 0, 0)}] = , [{[{[a[1] - 3/2]}, {[{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}]}]} , {[{[a[1] - 2]}, {[3]}]}] = , [{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[5](0, 0, 1, 0)}, {f[6](0, 1, 0, 0)}] = , [{[-1]}, {[-1]}] For the domain, {a[3] = 0, a[4] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{f[5](1, 0, 1, 0), f[5](0, 2, 0, 0)}, {f[6](1, 1, 0, 0)}] = , [{[1/2], [{[1/4]}, {[-1/4]}]}, {[{[0]}, {[{[0]}, {[3]}]}]}] = , [{[1/2]}, {[1/2]}] For the domain, {a[3] = 0, a[4] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[5](a[1] - 1, 2, 0, 0), f[5](a[1], 0, 1, 0)}, {f[6](a[1], 1, 0, 0)}] = , [{[a[1] - 1/2], [{[{[2 a[1] - 2]}, {[a[1] - 1/2]}]}, {[{[{[a[1] - 1]}, {[a[1] - 1]}]}, {[a[1] - 1]}]}]}, {[{[a[1] - 1]}, {[{[a[1] - 1]}, {[3]}]}]}] = , [{[a[1] - 1/2]}, {[{[a[1] - 1]}, {[{[a[1] - 1]}, {[3]}]}]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 2} The value of the game = , [{f[5](0, 1, 1, 0)}, {f[6](0, 2, 0, 0)}] = , [{[{[0]}, {[1/2]}]}, {[-1/4]}] = , [{[1/4]}, {[-1/4]}] For the domain, {a[3] = 0, a[4] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[5](a[1], 1, 1, 0), f[5](a[1] - 1, 3, 0, 0)}, {f[6](a[1], 2, 0, 0)}] = , [{[{[2 a[1]]}, {[a[1] + 1/2]}], [ {[{[2 a[1] - 1]}, {[a[1] - 1/2]}]}, {[ {[{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1] - 1]}] }]}, {[{[{[a[1]]}, {[a[1]]}]}, {[a[1]]}]}] = , [{[{[2 a[1]]}, {[a[1] + 1/2]}]}, {[{[{[a[1]]}, {[a[1]]}]}, {[a[1]]}]}] For the domain, {3 <= a[2], a[3] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [ {f[5](a[1] - 1, a[2] + 1, 0, 0), f[5](a[1], a[2] - 1, 1, 0)}, {f[6](a[1], a[2], 0, 0)}] = , [{[{[2 a[1] + a[2] - 2]}, {[a[1] + 1/2]}], [ {[{[2 a[1] + a[2] - 3]}, {[a[1] - 1/2]}]}, {[ {[{[{[2 a[1] - 4 + a[2]]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1] - 1]}]}]}, {[ {[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}]}] = , [{[{[2 a[1] + a[2] - 2]}, {[a[1] + 1/2]}]}, {[ {[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}]}] For the domain, {3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[5](0, a[2] - 1, 1, 0)}, {f[6](0, a[2], 0, 0)}] = , [{[{[-2 + a[2]]}, {[1/2]}]}, {[{[{[{[-3 + a[2]]}, {[1]}]}, {[0]}]}, {[0]}]}] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{f[2](0, 0, 0, 0, 0) + [0]}, {f[6](0, 0, 0, 1)}] = , [{[-5]}, {[-1]}] = , [-2] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 2} The value of the game = , [{f[2](0, 0, 0, 1, 0) + [0]}, {f[6](0, 0, 0, 2)}] = , [{[-3]}, {[-1]}] = , [-2] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, 3 <= a[4]} The value of the game = , [{f[2](0, 0, 0, a[4] - 1, 0) + [0]}, {f[6](0, 0, 0, a[4])}] = , [{[{[{[a[4] - 5]}, {[-1]}]}, {[-2]}]}, {[-1]}] = , [-2] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[2](1, 0, 0, 0, 0) + [0], f[5](0, 1, 0, 1)}, {f[6](1, 0, 0, 1)}] = , [{[-2], [-1/2]}, {[1/2]}] = , [0] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1, a[4] = 2} The value of the game = , [ {f[2](1, 0, 0, 1, 0) + [0], f[5](0, 1, 0, 2)}, {f[6](1, 0, 0, 2)}] = , [{[-1/2]}, {[1/2]}] = , [0] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1, 3 <= a[4]} The value of the game = , [ {f[5](0, 1, 0, a[4]), f[2](1, 0, 0, a[4] - 1, 0) + [0]}, {f[6](1, 0, 0, a[4])}] = , [{[-1/2], [{[{[a[4] - 3]}, {[1]}]}, {[0]}]}, {[1/2]}] = , [0] For the domain, {a[4] = 1, a[1] = 2, a[2] = 0, a[3] = 0} The value of the game = , [ {f[2](2, 0, 0, 0, 0) + [0], f[5](1, 1, 0, 1)}, {f[6](2, 0, 0, 1)}] = , [{[0], [{[1]}, {[1]}]}, {[3/2]}] = , [1] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 3} The value of the game = , [ {f[2](3, 0, 0, 0, 0) + [0], f[5](2, 1, 0, 1)}, {f[6](3, 0, 0, 1)}] = , [{[1], [{[2]}, {[2]}]}, {[5/2]}] = , [2] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 4} The value of the game = , [ {f[5](3, 1, 0, 1), f[2](4, 0, 0, 0, 0) + [0]}, {f[6](4, 0, 0, 1)}] = , [{[2], [{[3]}, {[3]}]}, {[7/2]}] = , [3] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, 5 <= a[1]} The value of the game = , [ {f[2](a[1], 0, 0, 0, 0) + [0], f[5](a[1] - 1, 1, 0, 1)}, {f[6](a[1], 0, 0, 1)}] = , [{[a[1] - 2], [{[a[1] - 1]}, {[a[1] - 1]}]}, {[{[a[1] - 1]}, {[5]}]}] = , [a[1] - 1] For the domain, {a[2] = 0, a[3] = 0, 2 <= a[1], a[4] = 2} The value of the game = , [ {f[5](a[1] - 1, 1, 0, 2), f[2](a[1], 0, 0, 1, 0) + [0]}, {f[6](a[1], 0, 0, 2)}] = , [{[{[a[1] - 1]}, {[a[1] - 1]}]}, {[a[1] - 1/2]}] = , [a[1] - 1] For the domain, {a[2] = 0, a[3] = 0, 2 <= a[1], 3 <= a[4]} The value of the game = , [{f[2](a[1], 0, 0, a[4] - 1, 0) + [0], f[5](a[1] - 1, 1, 0, a[4])}, {f[6](a[1], 0, 0, a[4])}] = , [{[{[a[1] - 1]}, {[a[1] - 1]}], [{[{[2 a[1] + a[4] - 5]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1] - 1/2]}] = , [a[1] - 1] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[2] = 1} The value of the game = , [ {f[5](0, 0, 1, 1), f[2](0, 1, 0, 0, 0) + [0]}, {f[6](0, 1, 0, 1)}] = , [{[-1], [{[-2]}, {[-2]}]}, {[0]}] = , [-1/2] For the domain, {a[1] = 0, a[3] = 0, a[2] = 1, a[4] = 2} The value of the game = , [ {f[2](0, 1, 0, 1, 0) + [0], f[5](0, 0, 1, 2)}, {f[6](0, 1, 0, 2)}] = , [{[-1]}, {[0]}] = , [-1/2] For the domain, {a[1] = 0, a[3] = 0, a[2] = 1, 3 <= a[4]} The value of the game = , [ {f[2](0, 1, 0, a[4] - 1, 0) + [0], f[5](0, 0, 1, a[4])}, {f[6](0, 1, 0, a[4])}] = , [{ [-1], [{[{[{[a[4] - 3]}, {[a[4] - 3]}]}, {[1/2]}]}, {[-1/2]}] }, {[0]}] = , [-1/2] For the domain, {a[4] = 1, a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[5](a[1], 0, 1, 1), f[5](a[1] - 1, 2, 0, 1), f[2](a[1], 1, 0, 0, 0) + [0]}, {f[6](a[1], 1, 0, 1)}] = , [{[a[1]], [{[a[1] - 1]}, {[a[1] - 1]}], [{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {a[3] = 0, a[2] = 1, 1 <= a[1], a[4] = 2} The value of the game = , [{f[5](a[1] - 1, 2, 0, 2), f[5](a[1], 0, 1, 2), f[2](a[1], 1, 0, 1, 0) + [0]}, {f[6](a[1], 1, 0, 2)}] = , [{[a[1]], [{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {a[3] = 0, a[2] = 1, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[5](a[1] - 1, 2, 0, a[4]), f[5](a[1], 0, 1, a[4]), f[2](a[1], 1, 0, a[4] - 1, 0) + [0]}, {f[6](a[1], 1, 0, a[4])}] = , [{[a[1]], [{[{[{[2 a[1] + a[4] - 3]}, {[2 a[1] + a[4] - 3]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]}, {[{[a[1]]}, {[a[1]]}]}], [{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {a[4] = 1, 3 <= a[2], a[3] = 0, 1 <= a[1]} The value of the game = , [{f[5](a[1], a[2] - 1, 1, 1), f[2](a[1], a[2], 0, 0, 0) + [0], f[5](a[1] - 1, a[2] + 1, 0, 1)}, {f[6](a[1], a[2], 0, 1)}] = , [{[a[1]], [{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}], [{[{[2 a[1] + a[2] - 3]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[4] = 1, a[3] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [{f[5](a[1], 1, 1, 1), f[5](a[1] - 1, 3, 0, 1), f[2](a[1], 2, 0, 0, 0) + [0]}, {f[6](a[1], 2, 0, 1)}] = , [{[a[1]], [{[{[2 a[1] - 1]}, {[a[1]]}]}, {[a[1] - 1]}], [{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] = , [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[3] = 0, 1 <= a[1], a[2] = 2, a[4] = 2} The value of the game = , [{f[2](a[1], 2, 0, 1, 0) + [0], f[5](a[1], 1, 1, 2), f[5](a[1] - 1, 3, 0, 2)}, {f[6](a[1], 2, 0, 2)}] = , [{[{[1 + a[1]]}, {[1 + a[1]]}], [{[{[2 a[1] - 1]}, {[a[1]]}]}, {[a[1] - 1]}], [{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] = , [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {3 <= a[2], a[3] = 0, 1 <= a[1], a[4] = 2} The value of the game = , [{f[5](a[1] - 1, a[2] + 1, 0, 2), f[5](a[1], a[2] - 1, 1, 2), f[2](a[1], a[2], 0, 1, 0) + [0]}, {f[6](a[1], a[2], 0, 2)}] = , [{[{[1 + a[1]]}, {[1 + a[1]]}], [{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}], [{[{[2 a[1] + a[2] - 3]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {2 <= a[2], a[3] = 0, 1 <= a[1], a[4] = 3} The value of the game = , [{f[2](a[1], a[2], 0, 2, 0) + [0], f[5](a[1] - 1, a[2] + 1, 0, 3), f[5](a[1], a[2] - 1, 1, 3)}, {f[6](a[1], a[2], 0, 3)}] = , [{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}], [{[ {[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}], [{[{[2 a[1] + a[2] - 3]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] %1 := {[2 a[1] + a[2] - 1]} = , [{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {2 <= a[2], a[3] = 0, 1 <= a[1], 4 <= a[4]} The value of the game = , [{f[2](a[1], a[2], 0, a[4] - 1, 0) + [0], f[5](a[1] - 1, a[2] + 1, 0, a[4]), f[5](a[1], a[2] - 1, 1, a[4])}, {f[6](a[1], a[2], 0, a[4])}] = , [{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}], [{[{ [{[2 a[1] + a[2] + a[4] - 4]}, {[2 a[1] + a[2] + a[4] - 4]}]} , {[{[{[2 a[1] + a[2] - 1]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}]} , {[{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}], [{[{[2 a[1] + a[2] - 3]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[{[2 a[1] + a[2] - 2]}, {[1 + a[1]]}]}, {[a[1]]}] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[2] = 2} The value of the game = , [ {f[2](0, 2, 0, 0, 0) + [0], f[5](0, 1, 1, 1)}, {f[6](0, 2, 0, 1)}] = , [{[{[-1/2]}, {[-1/2]}], [{[0]}, {[1]}]}, {[0]}] = , [{[1/2]}, {[0]}] For the domain, {a[4] = 1, 3 <= a[2], a[1] = 0, a[3] = 0} The value of the game = , [ {f[2](0, a[2], 0, 0, 0) + [0], f[5](0, a[2] - 1, 1, 1)}, {f[6](0, a[2], 0, 1)}] = , [{[0], [{[-2 + a[2]]}, {[1]}]}, {[0]}] = , [{[{[-2 + a[2]]}, {[1]}]}, {[0]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 2, a[4] = 2} The value of the game = , [ {f[2](0, 2, 0, 1, 0) + [0], f[5](0, 1, 1, 2)}, {f[6](0, 2, 0, 2)}] = , [{[1/2], [{[0]}, {[1]}]}, {[0]}] = , [{[1/2]}, {[0]}] For the domain, {3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 2} The value of the game = , [ {f[2](0, a[2], 0, 1, 0) + [0], f[5](0, a[2] - 1, 1, 2)}, {f[6](0, a[2], 0, 2)}] = , [{[{[1]}, {[1]}], [{[-2 + a[2]]}, {[1]}]}, {[0]}] = , [{[{[-2 + a[2]]}, {[1]}]}, {[0]}] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, a[4] = 3} The value of the game = , [ {f[2](0, a[2], 0, 2, 0) + [0], f[5](0, a[2] - 1, 1, 3)}, {f[6](0, a[2], 0, 3)}] = , [{[{[{[{[a[2] - 1]}, {[a[2] - 1]}], [{[a[2] - 1]}, {[{[a[2] - 1]}, {[2]}]}]}, {[{[a[2] - 1]}, {[1]}], [{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}, {[{[{[-2 + a[2]]}, {[1]}]}, {[0]}]}], [{[-2 + a[2]]}, {[1]}]} , {[0]}] = , [{[{[-2 + a[2]]}, {[1]}]}, {[0]}] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, 4 <= a[4]} The value of the game = , [{f[5](0, a[2] - 1, 1, a[4]), f[2](0, a[2], 0, a[4] - 1, 0) + [0]}, {f[6](0, a[2], 0, a[4])}] = , [{[{[-2 + a[2]]}, {[1]}], [{[ {[{[-4 + a[2] + a[4]]}, {[-4 + a[2] + a[4]]}]}, {[{[{[a[2] - 1]}, {[2]}]}, {[1]}]}]}, {[{[{[-2 + a[2]]}, {[1]}]}, {[0]}]}]}, {[0]}] = , [{[{[-2 + a[2]]}, {[1]}]}, {[0]}] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{}, {f[6](0, 0, 1, 0)}] = , [{}, {[{[-1]}, {[-1]}]}] = , [-1] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{f[5](a[1] - 1, 1, 1, 0)}, {f[6](a[1], 0, 1, 0)}] = , [{[{[2 a[1] - 2]}, {[a[1] - 1/2]}]}, {[a[1]]}] = , [a[1] - 1/2] For the domain, {a[3] = 1, a[4] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [ {f[5](a[1] - 1, a[2] + 1, 1, 0), f[5](a[1], a[2] - 1, 2, 0)}, {f[6](a[1], a[2], 1, 0)}] = , [{[2 a[1] + a[2] - 1], [{[2 a[1] + a[2] - 2]}, {[a[1] - 1/2]}] }, {[a[1] + 1/2]}] = , [{[2 a[1] + a[2] - 1]}, {[a[1] + 1/2]}] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[5](0, a[2] - 1, 2, 0)}, {f[6](0, a[2], 1, 0)}] = , [{[a[2] - 1]}, {[1/2]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 0} The value of the game = , [{f[2](0, 0, 1, 0, 0) + [0]}, {f[6](0, 0, 1, 1)}] = , [{[-2]}, {[0]}] = , [-1] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 2} The value of the game = , [{f[2](0, 0, 1, 1, 0) + [0]}, {f[6](0, 0, 1, 2)}] = , [{[{[-1]}, {[-1]}]}, {[0]}] = , [-1] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, 3 <= a[4]} The value of the game = , [{f[2](0, 0, 1, a[4] - 1, 0) + [0]}, {f[6](0, 0, 1, a[4])}] = , [{[{[{[a[4] - 3]}, {[0]}]}, {[-1]}]}, {[0]}] = , [-1] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, 1 <= a[1]} The value of the game = , [ {f[2](a[1], 0, 1, 0, 0) + [0], f[5](a[1] - 1, 1, 1, 1)}, {f[6](a[1], 0, 1, 1)}] = , [{[a[1] - 1], [{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] + 1/2]}] = , [a[1]] For the domain, {a[3] = 1, a[2] = 0, a[1] = 1, a[4] = 2} The value of the game = , [ {f[5](0, 1, 1, 2), f[2](1, 0, 1, 1, 0) + [0]}, {f[6](1, 0, 1, 2)}] = , [{[{[1]}, {[1]}], [{[0]}, {[1]}]}, {[3/2]}] = , [1] For the domain, {a[3] = 1, a[2] = 0, 2 <= a[1], a[4] = 2} The value of the game = , [ {f[5](a[1] - 1, 1, 1, 2), f[2](a[1], 0, 1, 1, 0) + [0]}, {f[6](a[1], 0, 1, 2)}] = , [{[{[{[{[2 a[1] - 2]}, {[2 a[1] - 2]}]}, {[a[1] + 1/2]}]}, {[a[1]]}], [{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] + 1/2]}] = , [a[1]] For the domain, {a[3] = 1, a[2] = 0, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[2](a[1], 0, 1, a[4] - 1, 0) + [0], f[5](a[1] - 1, 1, 1, a[4])}, {f[6](a[1], 0, 1, a[4])}] = , [{[{[2 a[1] - 2]}, {[a[1]]}], [{[{[2 a[1] + a[4] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1] + 1/2]}] = , [a[1]] For the domain, {a[3] = 1, a[4] = 1, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[5](a[1], 0, 2, 1), f[2](a[1], 1, 1, 0, 0) + [0], f[5](a[1] - 1, 2, 1, 1)}, {f[6](a[1], 1, 1, 1)}] = , [{[{[2 a[1] - 1]}, {[a[1]]}], [2 a[1]]}, {[1 + a[1]]}] = , [{[2 a[1]]}, {[1 + a[1]]}] For the domain, {a[3] = 1, a[4] = 1, 2 <= a[2], 1 <= a[1]} The value of the game = , [{f[5](a[1], a[2] - 1, 2, 1), f[5](a[1] - 1, a[2] + 1, 1, 1), f[2](a[1], a[2], 1, 0, 0) + [0]}, {f[6](a[1], a[2], 1, 1)}] = , [{[2 a[1] + a[2] - 1], [{[2 a[1] + a[2] - 3/2]}, {[a[1]]}], [{[2 a[1] + a[2] - 2]}, {[a[1]]}]}, {[1 + a[1]]}] = , [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}] For the domain, {a[3] = 1, a[2] = 1, 1 <= a[1], a[4] = 2} The value of the game = , [{f[5](a[1] - 1, 2, 1, 2), f[5](a[1], 0, 2, 2), f[2](a[1], 1, 1, 1, 0) + [0]}, {f[6](a[1], 1, 1, 2)}] = , [{[{[2 a[1] - 1]}, {[a[1]]}], [2 a[1]], [{[{[2 a[1]]}, {[2 a[1]]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}]} , {[1 + a[1]]}] = , [{[2 a[1]]}, {[1 + a[1]]}] For the domain, {a[3] = 1, 2 <= a[2], 1 <= a[1], a[4] = 2} The value of the game = , [{f[5](a[1], a[2] - 1, 2, 2), f[5](a[1] - 1, a[2] + 1, 1, 2), f[2](a[1], a[2], 1, 1, 0) + [0]}, {f[6](a[1], a[2], 1, 2)}] = , [{[{[{[2 a[1] + a[2] - 1]}, {[2 a[1] + a[2] - 1]}]}, {[{[1 + a[1]]}, {[1 + a[1]]}]}], [2 a[1] + a[2] - 1], [{[2 a[1] + a[2] - 2]}, {[a[1]]}]}, {[1 + a[1]]}] = , [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}] For the domain, {a[3] = 1, 1 <= a[1], 1 <= a[2], 3 <= a[4]} The value of the game = , [{f[5](a[1], a[2] - 1, 2, a[4]), f[5](a[1] - 1, a[2] + 1, 1, a[4]), f[2](a[1], a[2], 1, a[4] - 1, 0) + [0]}, {f[6](a[1], a[2], 1, a[4])}] = , [{[2 a[1] + a[2] - 1], [{[{[2 a[1] + a[2] + a[4] - 3]}, {[{[2 a[1] + a[2]]}, {[a[1] + 2]}]}]}, {[a[1] + 2], [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}]}], [{[2 a[1] + a[2] - 2]}, {[a[1]]}]}, {[1 + a[1]]}] = , [{[2 a[1] + a[2] - 1]}, {[1 + a[1]]}] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 1} The value of the game = , [ {f[2](0, 1, 1, 0, 0) + [0], f[5](0, 0, 2, 1)}, {f[6](0, 1, 1, 1)}] = , [{[0], [{[-1]}, {[0]}]}, {[1]}] = , [1/2] For the domain, {a[3] = 1, a[4] = 1, 2 <= a[2], a[1] = 0} The value of the game = , [ {f[2](0, a[2], 1, 0, 0) + [0], f[5](0, a[2] - 1, 2, 1)}, {f[6](0, a[2], 1, 1)}] = , [{[{[- 3/2 + a[2]]}, {[0]}], [a[2] - 1]}, {[1]}] = , [{[a[2] - 1]}, {[1]}] For the domain, {a[3] = 1, a[1] = 0, a[2] = 1, a[4] = 2} The value of the game = , [ {f[2](0, 1, 1, 1, 0) + [0], f[5](0, 0, 2, 2)}, {f[6](0, 1, 1, 2)}] = , [{[0], [{[1/2]}, {[1/2]}]}, {[1]}] = , [1/2] For the domain, {a[3] = 1, 2 <= a[2], a[1] = 0, a[4] = 2} The value of the game = , [ {f[5](0, a[2] - 1, 2, 2), f[2](0, a[2], 1, 1, 0) + [0]}, {f[6](0, a[2], 1, 2)}] = , [{[{[{[a[2] - 1]}, {[a[2] - 1]}]}, {[{[1]}, {[1]}]}], [a[2] - 1]}, {[1]}] = , [{[a[2] - 1]}, {[1]}] For the domain, {a[3] = 1, a[1] = 0, 1 <= a[2], 3 <= a[4]} The value of the game = , [{f[5](0, a[2] - 1, 2, a[4]), f[2](0, a[2], 1, a[4] - 1, 0) + [0]}, {f[6](0, a[2], 1, a[4])}] = , [{[a[2] - 1], [{[{[-3 + a[2] + a[4]]}, {[{[a[2]]}, {[2]}]}]}, {[2], [{[a[2] - 1]}, {[1]}]}]}, {[1]}] = , [{[a[2] - 1]}, {[1]}] For the domain, {a[4] = 1, 1 <= a[1], a[3] = 2, 1 <= a[2]} The value of the game = , [{f[5](a[1], a[2] - 1, 3, 1), f[5](a[1] - 1, a[2] + 1, 2, 1), f[2](a[1], a[2], 2, 0, 0) + [0]}, {}] = , [{[2 a[1] + a[2] - 1], [2 a[1] + a[2] - 1/2]}, {}] = , [2 a[1] + a[2]] For the domain, {a[4] = 1, 1 <= a[1], 1 <= a[2], a[3] = 3} The value of the game = , [{f[2](a[1], a[2], 3, 0, 0) + [0], f[5](a[1], a[2] - 1, 4, 1), f[5](a[1] - 1, a[2] + 1, 3, 1)}, {}] = , [{[2 a[1] + a[2] - 1], [ {[{[{[3 a[1] + 2 a[2]]}, {[%1, {[%1, {[a[1] + 2]}]}]}]}, %1]} , %1]}, {}] %1 := {[2 a[1] + a[2]]} = , [2 a[1] + a[2]] For the domain, {a[4] = 1, 1 <= a[1], 1 <= a[2], 4 <= a[3]} The value of the game = , [{f[2](a[1], a[2], a[3], 0, 0) + [0], f[5](a[1] - 1, a[2] + 1, a[3], 1), f[5](a[1], a[2] - 1, a[3] + 1, 1)}, {}] = , [{[2 a[1] + a[2] - 1], [{[ {[{[3 a[1] + 2 a[2] + a[3] - 3]}, {[2 a[1] + a[2] + 1/2]}]}, {[2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}]}, {}] = , [2 a[1] + a[2]] For the domain, {2 <= a[3], 1 <= a[1], 1 <= a[2], a[4] = 2} The value of the game = , [{f[5](a[1] - 1, a[2] + 1, a[3], 2), f[5](a[1], a[2] - 1, a[3] + 1, 2), f[2](a[1], a[2], a[3], 1, 0) + [0]}, {}] = , [{[{[2 a[1] + a[2]]}, {[2 a[1] + a[2]]}], [2 a[1] + a[2] - 1]} , {}] = , [2 a[1] + a[2]] For the domain, {2 <= a[3], 1 <= a[1], 1 <= a[2], 3 <= a[4]} The value of the game = , [{f[5](a[1] - 1, a[2] + 1, a[3], a[4]), f[5](a[1], a[2] - 1, a[3] + 1, a[4]), f[2](a[1], a[2], a[3], a[4] - 1, 0) + [0]}, {}] = , [{[2 a[1] + a[2] - 1], [ {[{[2 a[1] + a[2] + a[4] - 3]}, {[1 + 2 a[1] + a[2]]}]}, {[2 a[1] + a[2]]}]}, {}] = , [2 a[1] + a[2]] For the domain, {2 <= a[3], a[4] = 0, 1 <= a[1], 1 <= a[2]} The value of the game = , [{f[5](a[1] - 1, a[2] + 1, a[3], 0), f[5](a[1], a[2] - 1, a[3] + 1, 0)}, {}] = , [{[2 a[1] + a[2] - 1]}, {}] = , [2 a[1] + a[2]] For the domain, {a[4] = 1, a[2] = 0, 1 <= a[1], a[3] = 2} The value of the game = , [{f[2](a[1], 0, 2, 0, 0) + [0], f[5](a[1] - 1, 1, 2, 1)}, {}] = , [{[2 a[1] - 1]}, {}] = , [2 a[1]] For the domain, {a[4] = 1, a[2] = 0, 1 <= a[1], a[3] = 3} The value of the game = , [{f[5](a[1] - 1, 1, 3, 1), f[2](a[1], 0, 3, 0, 0) + [0]}, {}] = , [{[2 a[1] - 1], [{[{[2 a[1]]}, {[2 a[1]]}]}, {[2 a[1]]}]}, {}] = , [2 a[1]] For the domain, {a[4] = 1, a[2] = 0, 1 <= a[1], 4 <= a[3]} The value of the game = , [ {f[5](a[1] - 1, 1, a[3], 1), f[2](a[1], 0, a[3], 0, 0) + [0]} , {}] = , [{[2 a[1] - 1], [ {[{[{[3 a[1] - 3 + a[3]]}, {[2 a[1] + 1/2]}]}, {[2 a[1]]}]}, {[2 a[1]]}]}, {}] = , [2 a[1]] For the domain, {2 <= a[3], a[2] = 0, 1 <= a[1], a[4] = 2} The value of the game = , [ {f[2](a[1], 0, a[3], 1, 0) + [0], f[5](a[1] - 1, 1, a[3], 2)} , {}] = , [{[2 a[1] - 1], [{[2 a[1]]}, {[2 a[1]]}]}, {}] = , [2 a[1]] For the domain, {2 <= a[3], a[2] = 0, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[2](a[1], 0, a[3], a[4] - 1, 0) + [0], f[5](a[1] - 1, 1, a[3], a[4])}, {}] = , [{[2 a[1] - 1], [{[{[2 a[1] + a[4] - 3]}, {[1 + 2 a[1]]}]}, {[2 a[1]]}]}, {}] = , [2 a[1]] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [{f[5](a[1] - 1, 1, a[3], 0)}, {}] = , [{[2 a[1] - 1]}, {}] = , [2 a[1]] For the domain, {a[4] = 1, a[1] = 0, a[3] = 2, 1 <= a[2]} The value of the game = , [{f[2](0, a[2], 2, 0, 0) + [0], f[5](0, a[2] - 1, 3, 1)}, {}] = , [{[a[2] - 1], [- 1/2 + a[2]]}, {}] = , [a[2]] For the domain, {a[4] = 1, a[1] = 0, 1 <= a[2], a[3] = 3} The value of the game = , [{f[5](0, a[2] - 1, 4, 1), f[2](0, a[2], 3, 0, 0) + [0]}, {}] = , [{[a[2] - 1], [{ [{[{[2 a[2]]}, {[{[a[2]]}, {[{[a[2]]}, {[2]}]}]}]}, {[a[2]]}] }, {[a[2]]}]}, {}] = , [a[2]] For the domain, {a[4] = 1, a[1] = 0, 1 <= a[2], 4 <= a[3]} The value of the game = , [{f[5](0, a[2] - 1, a[3] + 1, 1), f[2](0, a[2], a[3], 0, 0) + [0]}, {}] = , [{[{[{[{[-3 + 2 a[2] + a[3]]}, {[1/2 + a[2]]}]}, {[a[2]]}]}, {[a[2]]}], [a[2] - 1]}, {}] = , [a[2]] For the domain, {2 <= a[3], a[1] = 0, 1 <= a[2], a[4] = 2} The value of the game = , [{f[5](0, a[2] - 1, a[3] + 1, 2), f[2](0, a[2], a[3], 1, 0) + [0]}, {}] = , [{[a[2] - 1], [{[a[2]]}, {[a[2]]}]}, {}] = , [a[2]] For the domain, {2 <= a[3], a[1] = 0, 1 <= a[2], 3 <= a[4]} The value of the game = , [{f[5](0, a[2] - 1, a[3] + 1, a[4]), f[2](0, a[2], a[3], a[4] - 1, 0) + [0]}, {}] = , [{[{[{[-3 + a[2] + a[4]]}, {[a[2] + 1]}]}, {[a[2]]}], [a[2] - 1]}, {}] = , [a[2]] For the domain, {2 <= a[3], a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [{f[5](0, a[2] - 1, a[3] + 1, 0)}, {}] = , [{[a[2] - 1]}, {}] = , [a[2]] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 2} The value of the game = , [{f[2](0, 0, 2, 0, 0) + [0]}, {}] = , [{[-1]}, {}] = , [0] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 3} The value of the game = , [{f[2](0, 0, 3, 0, 0) + [0]}, {}] = , [{[{[{[0]}, {[0]}]}, {[0]}]}, {}] = , [0] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, 4 <= a[3]} The value of the game = , [{f[2](0, 0, a[3], 0, 0) + [0]}, {}] = , [{[{[{[{[-3 + a[3]]}, {[1/2]}]}, {[0]}]}, {[0]}]}, {}] = , [0] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 2} The value of the game = , [{f[2](0, 0, a[3], 1, 0) + [0]}, {}] = , [{[{[0]}, {[0]}]}, {}] = , [0] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, 3 <= a[4]} The value of the game = , [{f[2](0, 0, a[3], a[4] - 1, 0) + [0]}, {}] = , [{[{[{[a[4] - 3]}, {[1]}]}, {[0]}]}, {}] = , [0] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{}, {}] = , [{}, {}] = , [0] ########## #, f[6], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{}, {f[8](0, 0, 0) + [0], f[7](0, 0, 0, 0)}] = , [{}, {[-2]}] = , [-3] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[6](0, 1, 0, 0)}, {f[8](1, 0, 0) + [0], f[7](1, 0, 0, 0)}] = , [{[-1]}, {[-1], [{[0]}, {[-1/2]}]}] = , [{[-1]}, {[-1]}] For the domain, {a[1] = 2, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[6](1, 1, 0, 0)}, {f[8](2, 0, 0) + [0], f[7](2, 0, 0, 0)}] = , [{[{[0]}, {[{[0]}, {[3]}]}]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 3} The value of the game = , [{f[6](2, 1, 0, 0)}, {f[7](3, 0, 0, 0), f[8](3, 0, 0) + [0]}] = , [{[{[1]}, {[{[1]}, {[3]}]}]}, {[{[2]}, {[2]}]}] = , [2] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 4} The value of the game = , [{f[6](3, 1, 0, 0)}, {f[7](4, 0, 0, 0), f[8](4, 0, 0) + [0]}] = , [{[{[2]}, {[{[2]}, {[3]}]}]}, {[11/4], [{[3]}, {[3]}]}] = , [5/2] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, 5 <= a[1]} The value of the game = , [{f[6](a[1] - 1, 1, 0, 0)}, {f[8](a[1], 0, 0) + [0], f[7](a[1], 0, 0, 0)}] = , [{[{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}]}, {[3], [{[a[1] - 1]}, {[a[1] - 1]}]}] = , [{[a[1] - 2]}, {[3]}] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[6](0, 0, 0, 1)}, {f[8](0, 0, 1) + [0], f[7](0, 0, 1, 0)}] = , [{[-1]}, {[-1], [{[0]}, {[0]}]}] = , [{[-1]}, {[-1]}] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[6](0, 0, a[3] - 1, 1)}, {f[8](0, 0, a[3]) + [0], f[7](0, 0, a[3], 0)}] = , [{[a[3] - 2]}, {[a[3] - 2], [{[a[3] - 1]}, {[a[3] - 1]}]}] = , [{[a[3] - 2]}, {[a[3] - 2]}] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[6](1, 0, 0, 1), f[6](0, 1, 1, 0)}, {f[8](1, 0, 1) + [0], f[7](1, 0, 1, 0)}] = , [{[1/2]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[3] = 1, a[1] = 2, a[2] = 0, a[4] = 0} The value of the game = , [{f[6](2, 0, 0, 1), f[6](1, 1, 1, 0)}, {f[7](2, 0, 1, 0), f[8](2, 0, 1) + [0]}] = , [{[3/2]}, {[{[2]}, {[2]}]}] = , [2] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 3} The value of the game = , [{f[6](3, 0, 0, 1), f[6](2, 1, 1, 0)}, {f[8](3, 0, 1) + [0], f[7](3, 0, 1, 0)}] = , [{[5/2]}, {[{[3]}, {[3]}]}] = , [3] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 4} The value of the game = , [{f[6](4, 0, 0, 1), f[6](3, 1, 1, 0)}, {f[7](4, 0, 1, 0), f[8](4, 0, 1) + [0]}] = , [{[7/2]}, {[{[4]}, {[4]}]}] = , [4] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, 5 <= a[1]} The value of the game = , [ {f[6](a[1], 0, 0, 1), f[6](a[1] - 1, 1, 1, 0)}, {f[8](a[1], 0, 1) + [0], f[7](a[1], 0, 1, 0)}] = , [{[a[1] - 1/2], [{[a[1] - 1]}, {[5]}]}, {[{[a[1]]}, {[a[1]]}]} ] = , [a[1]] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [ {f[6](a[1] - 1, 1, a[3], 0), f[6](a[1], 0, a[3] - 1, 1)}, {f[7](a[1], 0, a[3], 0), f[8](a[1], 0, a[3]) + [0]}] = , [{[a[1] - 3/2 + a[3]]}, {[{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}]}] = , [a[1] + a[3] - 1] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[5](0, 0, 0, 1)}, {f[8](0, 1, 0) + [0], f[7](0, 1, 0, 0)}] = , [{[-2]}, {[{[-1]}, {[3]}], [{[{[0]}, {[0]}]}, {[3]}]}] = , [-1] For the domain, {a[3] = 0, a[4] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{f[5](1, 0, 0, 1), f[6](0, 2, 0, 0)}, {f[7](1, 1, 0, 0), f[8](1, 1, 0) + [0]}] = , [{[0], [-1/4]}, {[{[0]}, {[3]}], [{[{[1]}, {[1]}]}, {[3]}]}] = , [1/2] For the domain, {a[3] = 0, a[4] = 0, 2 <= a[1], a[2] = 1} The value of the game = , [ {f[6](a[1] - 1, 2, 0, 0), f[5](a[1], 0, 0, 1)}, {f[7](a[1], 1, 0, 0), f[8](a[1], 1, 0) + [0]}] = , [{[a[1] - 1], [{[{[a[1] - 1]}, {[a[1] - 1]}]}, {[a[1] - 1]}]}, {[{[a[1] - 1]}, {[3]}], [{[{[a[1]]}, {[a[1]]}]}, {[3]}]}] = , [{[a[1] - 1]}, {[{[a[1] - 1]}, {[3]}]}] For the domain, {a[1] = 0, a[3] = 0, a[4] = 0, a[2] = 2} The value of the game = , [{f[5](0, 1, 0, 1)}, {f[8](0, 2, 0) + [0]}] = , [{[-1/2]}, {[0]}] = , [-1/4] For the domain, {a[3] = 0, a[4] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [ {f[5](a[1], 1, 0, 1), f[6](a[1] - 1, 3, 0, 0)}, {f[8](a[1], 2, 0) + [0]}] = , [{[ {[{[{[2 a[1] - 2]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1] - 1]}] , [{[a[1]]}, {[a[1]]}]}, {[a[1]]}] = , [{[{[a[1]]}, {[a[1]]}]}, {[a[1]]}] For the domain, {3 <= a[2], a[3] = 0, a[4] = 0, 1 <= a[1]} The value of the game = , [ {f[5](a[1], a[2] - 1, 0, 1), f[6](a[1] - 1, a[2] + 1, 0, 0)}, {f[8](a[1], a[2], 0) + [0]}] = , [{[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}], [ {[{[{[2 a[1] - 4 + a[2]]}, {[a[1]]}]}, {[a[1] - 1]}]}, {[a[1] - 1]}]}, {[a[1]]}] = , [{[{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1]]}] For the domain, {3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[5](0, a[2] - 1, 0, 1)}, {f[8](0, a[2], 0) + [0]}] = , [{[{[{[-3 + a[2]]}, {[1]}]}, {[0]}]}, {[0]}] For the domain, {a[3] = 1, a[4] = 0, a[1] = 1, a[2] = 1} The value of the game = , [{f[6](0, 2, 1, 0), f[6](1, 1, 0, 1)}, {f[7](1, 1, 1, 0), f[8](1, 1, 1) + [0]}] = , [{[1/2], [1]}, {[2], [{[3]}, {[3]}]}] = , [3/2] For the domain, {a[3] = 1, a[1] = 2, a[4] = 0, a[2] = 1} The value of the game = , [{f[6](2, 1, 0, 1), f[6](1, 2, 1, 0)}, {f[8](2, 1, 1) + [0], f[7](2, 1, 1, 0)}] = , [{[2], [3/2]}, {[3], [{[4]}, {[4]}]}] = , [5/2] For the domain, {a[3] = 1, a[4] = 0, a[2] = 1, a[1] = 3} The value of the game = , [{f[6](3, 1, 0, 1), f[6](2, 2, 1, 0)}, {f[7](3, 1, 1, 0), f[8](3, 1, 1) + [0]}] = , [{[3], [5/2]}, {[4], [{[9/2]}, {[9/2]}]}] = , [7/2] For the domain, {a[3] = 1, a[4] = 0, a[2] = 1, 4 <= a[1]} The value of the game = , [ {f[6](a[1], 1, 0, 1), f[6](a[1] - 1, 2, 1, 0)}, {f[8](a[1], 1, 1) + [0], f[7](a[1], 1, 1, 0)}] = , [{[a[1]], [a[1] - 1/2]}, {[1 + a[1]]}] = , [a[1] + 1/2] For the domain, {2 <= a[3], a[4] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [ {f[6](a[1] - 1, 2, a[3], 0), f[6](a[1], 1, a[3] - 1, 1)}, {f[7](a[1], 1, a[3], 0), f[8](a[1], 1, a[3]) + [0]}] = , [{[a[1] - 3/2 + a[3]], [a[1] + a[3] - 1]}, {[a[1] + a[3]], [{[a[1] + 1 + a[3]]}, {[a[1] + 1 + a[3]]}]}] = , [a[1] - 1/2 + a[3]] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[6](0, 1, 0, 1)}, {f[7](0, 1, 1, 0), f[8](0, 1, 1) + [0]}] = , [{[0]}, {[1], [{[2]}, {[2]}]}] = , [1/2] For the domain, {2 <= a[3], a[1] = 0, a[4] = 0, a[2] = 1} The value of the game = , [{f[6](0, 1, a[3] - 1, 1)}, {f[8](0, 1, a[3]) + [0], f[7](0, 1, a[3], 0)}] = , [{[a[3] - 1]}, {[{[a[3] + 1]}, {[a[3] + 1]}], [a[3]]}] = , [- 1/2 + a[3]] For the domain, {2 <= a[2], a[4] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[6](a[1] - 1, a[2] + 1, a[3], 0), f[6](a[1], a[2], a[3] - 1, 1)}, {f[8](a[1], a[2], a[3]) + [0]}] = , [{[a[1] - 3/2 + a[3]], [a[1] + a[3] - 1]}, {[a[1] + a[3]]}] = , [a[1] - 1/2 + a[3]] For the domain, {2 <= a[2], a[1] = 0, a[4] = 0, 1 <= a[3]} The value of the game = , [{f[6](0, a[2], a[3] - 1, 1)}, {f[8](0, a[2], a[3]) + [0]}] = , [{[a[3] - 1]}, {[a[3]]}] = , [- 1/2 + a[3]] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{f[3](0, 0, 0, 0, 0) + [0]}, {f[7](0, 0, 0, 1), f[8](0, 0, 0) + [2]}] = , [{[-4]}, {[0]}] = , [-1] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 2} The value of the game = , [{f[3](0, 0, 0, 1, 0) + [0]}, {f[7](0, 0, 0, 2)}] = , [{[-2]}, {[0]}] = , [-1] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, 3 <= a[4]} The value of the game = , [{f[3](0, 0, 0, a[4] - 1, 0) + [0]}, {f[7](0, 0, 0, a[4])}] = , [{[{[{[a[4] - 4]}, {[0]}]}, {[-1]}]}, {[0]}] = , [-1] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, 1 <= a[3]} The value of the game = , [ {f[3](0, 0, a[3], 0, 0) + [0], f[6](0, 0, a[3] - 1, 2)}, {f[8](0, 0, a[3]) + [2], f[7](0, 0, a[3], 1)}] = , [{[a[3] - 2]}, {[a[3]]}] = , [a[3] - 1] For the domain, {a[1] = 0, a[2] = 0, 1 <= a[3], a[4] = 2} The value of the game = , [ {f[6](0, 0, a[3] - 1, 3), f[3](0, 0, a[3], 1, 0) + [0]}, {f[7](0, 0, a[3], 2)}] = , [{[a[3] - 2], [{[a[3] - 1]}, {[a[3] - 1]}]}, {[a[3]]}] = , [a[3] - 1] For the domain, {a[1] = 0, a[2] = 0, 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[6](0, 0, a[3] - 1, a[4] + 1), f[3](0, 0, a[3], a[4] - 1, 0) + [0]}, {f[7](0, 0, a[3], a[4])}] = , [{[{[{[2 a[3] + a[4] - 4]}, {[a[3]]}]}, {[a[3] - 1]}], [a[3] - 2]}, {[a[3]]}] = , [a[3] - 1] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[6](0, 1, 0, 1), f[3](1, 0, 0, 0, 0) + [0]}, {f[7](1, 0, 0, 1), f[8](1, 0, 0) + [2]}] = , [{[0], [-1]}, {[1], [{[2]}, {[3/2]}]}] = , [1/2] For the domain, {a[4] = 1, a[1] = 2, a[2] = 0, a[3] = 0} The value of the game = , [ {f[3](2, 0, 0, 0, 0) + [0], f[6](1, 1, 0, 1)}, {f[8](2, 0, 0) + [2], f[7](2, 0, 0, 1)}] = , [{[1], [{[0]}, {[{[0]}, {[3]}]}]}, {[2], [{[3]}, {[3]}]}] = , [3/2] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 3} The value of the game = , [ {f[3](3, 0, 0, 0, 0) + [0], f[6](2, 1, 0, 1)}, {f[8](3, 0, 0) + [2], f[7](3, 0, 0, 1)}] = , [{[2], [{[1]}, {[{[1]}, {[3]}]}]}, {[3], [{[4]}, {[4]}]}] = , [5/2] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 4} The value of the game = , [ {f[6](3, 1, 0, 1), f[3](4, 0, 0, 0, 0) + [0]}, {f[7](4, 0, 0, 1), f[8](4, 0, 0) + [2]}] = , [{[3], [{[2]}, {[{[2]}, {[3]}]}]}, {[4], [19/4]}] = , [7/2] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, 5 <= a[1]} The value of the game = , [ {f[3](a[1], 0, 0, 0, 0) + [0], f[6](a[1] - 1, 1, 0, 1)}, {f[8](a[1], 0, 0) + [2], f[7](a[1], 0, 0, 1)}] = , [{[a[1] - 1], [{[a[1] - 2]}, {[{[a[1] - 2]}, {[3]}]}]}, {[a[1]], [5]}] = , [{[a[1] - 1]}, {[5]}] For the domain, {a[4] = 1, a[2] = 0, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[6](a[1], 0, a[3] - 1, 2), f[3](a[1], 0, a[3], 0, 0) + [0], f[6](a[1] - 1, 1, a[3], 1)}, {f[7](a[1], 0, a[3], 1), f[8](a[1], 0, a[3]) + [2]}] = , [{[a[1] - 3/2 + a[3]], [a[1] + a[3] - 1]}, {[a[1] + a[3]], [{[a[1] + 1 + a[3]]}, {[a[1] + 1 + a[3]]}]}] = , [a[1] - 1/2 + a[3]] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1, a[4] = 2} The value of the game = , [ {f[6](0, 1, 0, 2), f[3](1, 0, 0, 1, 0) + [0]}, {f[7](1, 0, 0, 2)}] = , [{[0], [{[0]}, {[0]}]}, {[1]}] = , [1/2] For the domain, {a[1] = 2, a[2] = 0, a[3] = 0, a[4] = 2} The value of the game = , [ {f[3](2, 0, 0, 1, 0) + [0], f[6](1, 1, 0, 2)}, {f[7](2, 0, 0, 2)}] = , [{[1], [{[3/2]}, {[3/2]}]}, {[2]}] = , [3/2] For the domain, {a[2] = 0, a[3] = 0, a[4] = 2, a[1] = 3} The value of the game = , [ {f[3](3, 0, 0, 1, 0) + [0], f[6](2, 1, 0, 2)}, {f[7](3, 0, 0, 2)}] = , [{[2], [{[5/2]}, {[5/2]}]}, {[3]}] = , [5/2] For the domain, {a[2] = 0, a[3] = 0, a[4] = 2, a[1] = 4} The value of the game = , [ {f[3](4, 0, 0, 1, 0) + [0], f[6](3, 1, 0, 2)}, {f[7](4, 0, 0, 2)}] = , [{[3], [27/8]}, {[4]}] = , [7/2] For the domain, {a[2] = 0, a[3] = 0, a[4] = 2, 5 <= a[1]} The value of the game = , [ {f[6](a[1] - 1, 1, 0, 2), f[3](a[1], 0, 0, 1, 0) + [0]}, {f[7](a[1], 0, 0, 2)}] = , [{[a[1] - 1], [{[a[1] - 1]}, {[{[a[1] - 1]}, {[5]}]}]}, {[a[1]]}] = , [a[1] - 1/2] For the domain, {a[4] = 3, a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[6](0, 1, 0, 3), f[3](1, 0, 0, 2, 0) + [0]}, {f[7](1, 0, 0, 3)}] = , [{[0], [{[5/4]}, {[1/2]}]}, {[1]}] = , [1/2] For the domain, {a[4] = 3, a[1] = 2, a[2] = 0, a[3] = 0} The value of the game = , [ {f[3](2, 0, 0, 2, 0) + [0], f[6](1, 1, 0, 3)}, {f[7](2, 0, 0, 3)}] = , [{[1], [{[{[3]}, {[5/2]}]}, {[3/2]}]}, {[2]}] = , [3/2] For the domain, {a[4] = 3, a[2] = 0, a[3] = 0, a[1] = 3} The value of the game = , [ {f[3](3, 0, 0, 2, 0) + [0], f[6](2, 1, 0, 3)}, {f[7](3, 0, 0, 3)}] = , [{[2], [{[{[5]}, {[7/2]}]}, {[5/2]}]}, {[3]}] = , [5/2] For the domain, {a[4] = 3, a[2] = 0, a[3] = 0, a[1] = 4} The value of the game = , [ {f[6](3, 1, 0, 3), f[3](4, 0, 0, 2, 0) + [0]}, {f[7](4, 0, 0, 3)}] = , [{[3], [{[{[7]}, {[9/2]}]}, {[7/2]}]}, {[4]}] = , [7/2] For the domain, {a[4] = 3, a[2] = 0, a[3] = 0, a[1] = 5} The value of the game = , [ {f[6](4, 1, 0, 3), f[3](5, 0, 0, 2, 0) + [0]}, {f[7](5, 0, 0, 3)}] = , [{[{[{[9]}, {[11/2]}]}, {[9/2]}], [4]}, {[5]}] = , [9/2] For the domain, {a[4] = 3, a[2] = 0, a[3] = 0, a[1] = 6} The value of the game = , [ {f[3](6, 0, 0, 2, 0) + [0], f[6](5, 1, 0, 3)}, {f[7](6, 0, 0, 3)}] = , [{[5], [{[{[11]}, {[{[6]}, {[6]}]}]}, {[11/2]}]}, {[6]}] = , [11/2] For the domain, {a[4] = 3, a[2] = 0, a[3] = 0, 7 <= a[1]} The value of the game = , [ {f[6](a[1] - 1, 1, 0, 3), f[3](a[1], 0, 0, 2, 0) + [0]}, {f[7](a[1], 0, 0, 3)}] = , [{[a[1] - 1], [{[a[1]]}, {[a[1] - 1/2]}]}, {[a[1]]}] = , [a[1] - 1/2] For the domain, {a[2] = 0, a[3] = 0, 1 <= a[1], 4 <= a[4]} The value of the game = , [{f[3](a[1], 0, 0, a[4] - 1, 0) + [0], f[6](a[1] - 1, 1, 0, a[4])}, {f[7](a[1], 0, 0, a[4])}] = , [{[a[1] - 1], [{[{[2 a[1] + a[4] - 4]}, {[a[1] + 1/2]}]}, {[a[1] - 1/2]}]}, {[a[1]]}] = , [a[1] - 1/2] For the domain, {a[2] = 0, 1 <= a[1], 1 <= a[3], a[4] = 2} The value of the game = , [{f[3](a[1], 0, a[3], 1, 0) + [0], f[6](a[1] - 1, 1, a[3], 2), f[6](a[1], 0, a[3] - 1, 3)}, {f[7](a[1], 0, a[3], 2)}] = , [{[a[1] - 3/2 + a[3]], [{[a[1] - 1/2 + a[3]]}, {[a[1] - 1/2 + a[3]]}], [a[1] + a[3] - 1]}, {[a[1] + a[3]]}] = , [a[1] - 1/2 + a[3]] For the domain, {a[2] = 0, 1 <= a[1], 1 <= a[3], a[4] = 3} The value of the game = , [{f[3](a[1], 0, a[3], 2, 0) + [0], f[6](a[1] - 1, 1, a[3], 3), f[6](a[1], 0, a[3] - 1, 4)}, {f[7](a[1], 0, a[3], 3)}] = , [{[a[1] - 3/2 + a[3]], [ {[{[2 a[1] + 2 a[3] - 1]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}], [a[1] + a[3] - 1]}, {[a[1] + a[3]]}] = , [a[1] - 1/2 + a[3]] For the domain, {a[2] = 0, 1 <= a[1], 1 <= a[3], 4 <= a[4]} The value of the game = , [{f[3](a[1], 0, a[3], a[4] - 1, 0) + [0], f[6](a[1] - 1, 1, a[3], a[4]), f[6](a[1], 0, a[3] - 1, a[4] + 1)}, {f[7](a[1], 0, a[3], a[4])}] = , [{[a[1] - 3/2 + a[3]], [a[1] + a[3] - 1], [ {[{[2 a[1] + 2 a[3] + a[4] - 4]}, {[a[1] + a[3] + 1/2]}]}, {[a[1] - 1/2 + a[3]]}]}, {[a[1] + a[3]]}] = , [a[1] - 1/2 + a[3]] For the domain, {a[4] = 1, a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[6](a[1] - 1, 2, 0, 1), f[5](a[1], 0, 0, 2), f[3](a[1], 1, 0, 0, 0) + [0]}, {f[8](a[1], 1, 0) + [2], f[7](a[1], 1, 0, 1)}] = , [{[a[1] - 1]}, {[{[1 + a[1]]}, {[5]}]}] = , [a[1]] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[2] = 1} The value of the game = , [ {f[5](0, 0, 0, 2), f[3](0, 1, 0, 0, 0) + [0]}, {f[7](0, 1, 0, 1), f[8](0, 1, 0) + [2]}] = , [{[-2]}, {[{[1]}, {[5]}]}] = , [0] For the domain, {a[3] = 0, a[2] = 1, 1 <= a[1], a[4] = 2} The value of the game = , [{f[3](a[1], 1, 0, 1, 0) + [0], f[6](a[1] - 1, 2, 0, 2), f[5](a[1], 0, 0, 3)}, {f[7](a[1], 1, 0, 2)}] = , [{[a[1] - 1], [{[a[1]]}, {[a[1]]}]}, {[a[1] + 2]}] = , [a[1]] For the domain, {a[3] = 0, a[2] = 1, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[3](a[1], 1, 0, a[4] - 1, 0) + [0], f[6](a[1] - 1, 2, 0, a[4]), f[5](a[1], 0, 0, a[4] + 1)}, {f[7](a[1], 1, 0, a[4])}] = , [{[a[1] - 1], [{[{[2 a[1] + a[4] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1] + 2]}] = , [a[1]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 1, a[4] = 2} The value of the game = , [ {f[5](0, 0, 0, 3), f[3](0, 1, 0, 1, 0) + [0]}, {f[7](0, 1, 0, 2)}] = , [{[-2], [-1/2]}, {[2]}] = , [0] For the domain, {a[1] = 0, a[3] = 0, a[2] = 1, 3 <= a[4]} The value of the game = , [ {f[5](0, 0, 0, a[4] + 1), f[3](0, 1, 0, a[4] - 1, 0) + [0]}, {f[7](0, 1, 0, a[4])}] = , [{[-2], [{[{[a[4] - 3]}, {[1]}]}, {[0]}]}, {[2]}] = , [0] For the domain, {a[4] = 1, a[2] = 1, 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[3](a[1], 1, a[3], 0, 0) + [0], f[6](a[1] - 1, 2, a[3], 1), f[6](a[1], 1, a[3] - 1, 2)}, {f[7](a[1], 1, a[3], 1), f[8](a[1], 1, a[3]) + [2]}] = , [{[a[1] + a[3] - 1]}, {[a[1] + a[3] + 2]}] = , [a[1] + a[3]] For the domain, {a[4] = 1, a[1] = 0, a[2] = 1, 1 <= a[3]} The value of the game = , [ {f[3](0, 1, a[3], 0, 0) + [0], f[6](0, 1, a[3] - 1, 2)}, {f[8](0, 1, a[3]) + [2], f[7](0, 1, a[3], 1)}] = , [{[a[3] - 1]}, {[2 + a[3]]}] = , [a[3]] For the domain, {a[2] = 1, 1 <= a[1], 1 <= a[3], a[4] = 2} The value of the game = , [{f[3](a[1], 1, a[3], 1, 0) + [0], f[6](a[1] - 1, 2, a[3], 2), f[6](a[1], 1, a[3] - 1, 3)}, {f[7](a[1], 1, a[3], 2)}] = , [{[a[1] + a[3] - 1], [{[a[1] + a[3]]}, {[a[1] + a[3]]}]}, {[a[1] + 2 + a[3]]}] = , [a[1] + a[3]] For the domain, {a[2] = 1, 1 <= a[1], 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[6](a[1] - 1, 2, a[3], a[4]), f[6](a[1], 1, a[3] - 1, a[4] + 1), f[3](a[1], 1, a[3], a[4] - 1, 0) + [0]}, {f[7](a[1], 1, a[3], a[4])}] = , [{[a[1] + a[3] - 1], [ {[{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]}]}, {[a[1] + 2 + a[3]]}] = , [a[1] + a[3]] For the domain, {a[1] = 0, a[2] = 1, 1 <= a[3], a[4] = 2} The value of the game = , [ {f[6](0, 1, a[3] - 1, 3), f[3](0, 1, a[3], 1, 0) + [0]}, {f[7](0, 1, a[3], 2)}] = , [{[{[a[3]]}, {[a[3]]}], [a[3] - 1]}, {[2 + a[3]]}] = , [a[3]] For the domain, {a[1] = 0, a[2] = 1, 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[6](0, 1, a[3] - 1, a[4] + 1), f[3](0, 1, a[3], a[4] - 1, 0) + [0]}, {f[7](0, 1, a[3], a[4])}] = , [{[a[3] - 1], [{[{[2 a[3] + a[4] - 3]}, {[a[3] + 1]}]}, {[a[3]]}]}, {[2 + a[3]]}] = , [a[3]] For the domain, {a[4] = 1, a[3] = 0, 1 <= a[1], a[2] = 2} The value of the game = , [{f[6](a[1] - 1, 3, 0, 1), f[5](a[1], 1, 0, 2), f[3](a[1], 2, 0, 0, 0) + [0]}, {f[8](a[1], 2, 0) + [2]}] = , [{[a[1] - 1], [{[a[1]]}, {[a[1]]}]}, {[a[1] + 2]}] = , [a[1]] For the domain, {a[4] = 1, a[3] = 0, 1 <= a[1], 4 <= a[2]} The value of the game = , [{f[6](a[1] - 1, a[2] + 1, 0, 1), f[3](a[1], a[2], 0, 0, 0) + [0], f[5](a[1], a[2] - 1, 0, 2)}, {f[8](a[1], a[2], 0) + [2]}] = , [{[a[1] - 1], [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], [{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1] + 2]}] = , [a[1]] For the domain, {a[4] = 1, a[3] = 0, 1 <= a[1], a[2] = 3} The value of the game = , [{f[3](a[1], 3, 0, 0, 0) + [0], f[6](a[1] - 1, 4, 0, 1), f[5](a[1], 2, 0, 2)}, {f[8](a[1], 3, 0) + [2]}] = , [{[a[1] - 1], [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {[a[1] + 2]}] = , [a[1]] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[2] = 2} The value of the game = , [ {f[3](0, 2, 0, 0, 0) + [0], f[5](0, 1, 0, 2)}, {f[8](0, 2, 0) + [2]}] = , [{[-1/2]}, {[2]}] = , [0] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, a[2] = 3} The value of the game = , [ {f[5](0, 2, 0, 2), f[3](0, 3, 0, 0, 0) + [0]}, {f[8](0, 3, 0) + [2]}] = , [{[{[1/2]}, {[0]}], [{[{[0]}, {[1]}]}, {[0]}]}, {[2]}] = , [0] For the domain, {a[4] = 1, a[1] = 0, a[3] = 0, 4 <= a[2]} The value of the game = , [ {f[3](0, a[2], 0, 0, 0) + [0], f[5](0, a[2] - 1, 0, 2)}, {f[8](0, a[2], 0) + [2]}] = , [{[{[{[1]}, {[1]}]}, {[0]}], [{[{[-3 + a[2]]}, {[1]}]}, {[0]}] }, {[2]}] = , [0] For the domain, {a[3] = 0, 1 <= a[1], a[2] = 2, a[4] = 2} The value of the game = , [{f[6](a[1] - 1, 3, 0, 2), f[5](a[1], 1, 0, 3), f[3](a[1], 2, 0, 1, 0) + [0]}, {}] = , [{[a[1] - 1], [{[a[1]]}, {[a[1]]}], [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {}] = , [a[1]] For the domain, {a[3] = 0, 1 <= a[1], a[2] = 2, 3 <= a[4]} The value of the game = , [{f[3](a[1], 2, 0, a[4] - 1, 0) + [0], f[6](a[1] - 1, 3, 0, a[4]), f[5](a[1], 1, 0, a[4] + 1)}, {}] = , [{[a[1] - 1], [{[a[1]]}, {[a[1]]}], [{[{[2 a[1] + a[4] - 2]}, {[1 + a[1]]}]}, {[a[1]]}]}, {}] = , [a[1]] For the domain, {3 <= a[2], a[3] = 0, 1 <= a[1], a[4] = 2} The value of the game = , [{f[6](a[1] - 1, a[2] + 1, 0, 2), f[5](a[1], a[2] - 1, 0, 3), f[3](a[1], a[2], 0, 1, 0) + [0]}, {}] = , [{[a[1] - 1], [{[{[{[%1, %1], [%1, {[%1, {[a[1] + 2]}]}]}, {[%1, {[1 + a[1]]}], [{[%1, {[a[1] + 2]}]}, {[1 + a[1]]}]}]}, {[1 + a[1]]}]}, {[a[1]]}], [{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {}] %1 := {[2 a[1] + a[2] - 2]} = , [a[1]] For the domain, {3 <= a[2], a[3] = 0, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[6](a[1] - 1, a[2] + 1, 0, a[4]), f[3](a[1], a[2], 0, a[4] - 1, 0) + [0], f[5](a[1], a[2] - 1, 0, a[4] + 1)}, {}] = , [{[a[1] - 1], [{[{[2 a[1] + a[2] - 3]}, {[1 + a[1]]}]}, {[a[1]]}], [{[{[2 a[1] + a[2] - 4 + a[4]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {}] = , [a[1]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 2, a[4] = 2} The value of the game = , [{f[3](0, 2, 0, 1, 0) + [0], f[5](0, 1, 0, 3)}, {}] = , [{[-1/2], [{[1/2]}, {[0]}]}, {}] = , [0] For the domain, {a[1] = 0, a[3] = 0, a[2] = 2, 3 <= a[4]} The value of the game = , [ {f[3](0, 2, 0, a[4] - 1, 0) + [0], f[5](0, 1, 0, a[4] + 1)}, {}] = , [{[{[{[-2 + a[4]]}, {[1]}]}, {[0]}], [-1/2]}, {}] = , [0] For the domain, {3 <= a[2], a[1] = 0, a[3] = 0, a[4] = 2} The value of the game = , [{f[5](0, a[2] - 1, 0, 3), f[3](0, a[2], 0, 1, 0) + [0]}, {}] = , [{[{[{[{[{[-2 + a[2]]}, {[{[-2 + a[2]]}, {[2]}]}], [{[-2 + a[2]]}, {[-2 + a[2]]}]}, {[{[-2 + a[2]]}, {[1]}], [{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}]} , {[1]}]}, {[0]}], [{[{[-3 + a[2]]}, {[1]}]}, {[0]}]}, {}] = , [0] For the domain, {3 <= a[2], a[1] = 0, a[3] = 0, 3 <= a[4]} The value of the game = , [{f[3](0, a[2], 0, a[4] - 1, 0) + [0], f[5](0, a[2] - 1, 0, a[4] + 1)}, {}] = , [{[{[{[-3 + a[2]]}, {[1]}]}, {[0]}], [{[{[-4 + a[2] + a[4]]}, {[1]}]}, {[0]}]}, {}] = , [0] For the domain, {a[4] = 1, 2 <= a[2], 1 <= a[1], 1 <= a[3]} The value of the game = , [{f[6](a[1] - 1, a[2] + 1, a[3], 1), f[6](a[1], a[2], a[3] - 1, 2), f[3](a[1], a[2], a[3], 0, 0) + [0]}, {f[8](a[1], a[2], a[3]) + [2]}] = , [{[a[1] + a[3] - 1]}, {[a[1] + a[3] + 2]}] = , [a[1] + a[3]] For the domain, {a[4] = 1, 2 <= a[2], a[1] = 0, 1 <= a[3]} The value of the game = , [ {f[3](0, a[2], a[3], 0, 0) + [0], f[6](0, a[2], a[3] - 1, 2)} , {f[8](0, a[2], a[3]) + [2]}] = , [{[a[3] - 1]}, {[2 + a[3]]}] = , [a[3]] For the domain, {2 <= a[2], 1 <= a[1], 1 <= a[3], a[4] = 2} The value of the game = , [{f[6](a[1] - 1, a[2] + 1, a[3], 2), f[6](a[1], a[2], a[3] - 1, 3), f[3](a[1], a[2], a[3], 1, 0) + [0]}, {}] = , [{[a[1] + a[3] - 1], [{[a[1] + a[3]]}, {[a[1] + a[3]]}]}, {}] = , [a[1] + a[3]] For the domain, {2 <= a[2], 1 <= a[1], 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[6](a[1] - 1, a[2] + 1, a[3], a[4]), f[6](a[1], a[2], a[3] - 1, a[4] + 1), f[3](a[1], a[2], a[3], a[4] - 1, 0) + [0]}, {}] = , [{[a[1] + a[3] - 1], [{ [{[2 a[1] + a[2] + 2 a[3] + a[4] - 4]}, {[a[1] + 1 + a[3]]}]} , {[a[1] + a[3]]}]}, {}] = , [a[1] + a[3]] For the domain, {2 <= a[2], a[1] = 0, 1 <= a[3], a[4] = 2} The value of the game = , [ {f[6](0, a[2], a[3] - 1, 3), f[3](0, a[2], a[3], 1, 0) + [0]} , {}] = , [{[a[3] - 1], [{[a[3]]}, {[a[3]]}]}, {}] = , [a[3]] For the domain, {2 <= a[2], a[1] = 0, 1 <= a[3], 3 <= a[4]} The value of the game = , [{f[6](0, a[2], a[3] - 1, a[4] + 1), f[3](0, a[2], a[3], a[4] - 1, 0) + [0]}, {}] = , [{[a[3] - 1], [{[{[-4 + a[2] + 2 a[3] + a[4]]}, {[a[3] + 1]}]}, {[a[3]]}]}, {}] = , [a[3]] ########## #, f[7], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{}, {f[9](0, 0, 0) + [0]}] = , [{}, {[-1]}] = , [-2] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[6](0, 0, 1, 0)}, {f[9](1, 0, 0) + [0]}] = , [{[{[-1]}, {[-1]}]}, {[-1/2]}] = , [-1] For the domain, {a[2] = 0, a[3] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [{f[6](a[1] - 1, 0, 1, 0)}, {f[9](a[1], 0, 0) + [0]}] = , [{[a[1] - 1]}, {[{[{[a[1] - 1]}, {[a[1] - 1]}]}, {[0]}]}] = , [{[a[1] - 1]}, {[a[1] - 1]}] For the domain, {a[3] = 0, a[4] = 0, a[2] = 1, 0 <= a[1]} The value of the game = , [{f[7](a[1], 0, 1, 0)}, {f[9](a[1], 1, 0) + [0]}] = , [{[{[a[1]]}, {[a[1]]}]}, {[{[{[{[a[1]]}, {[a[1]]}]}, {[3]}]}, {[2]}]}] = , [{[{[a[1]]}, {[a[1]]}]}, {[3]}] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0, a[4] = 0} The value of the game = , [{f[7](0, a[2] - 1, 1, 0)}, {f[9](0, a[2], 0) + [0]}] = , [{[{[2 a[2] - 2]}, {[2 a[2] - 2]}]}, {[{[{[-3 + 2 a[2]]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}] = , [2 a[2] - 2] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[7](1, a[2] - 1, 1, 0)}, {f[9](1, a[2], 0) + [0]}] = , [{[{[2 a[2] - 1]}, {[2 a[2] - 1]}]}, {[{[{[2 a[2] - 2]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}] = , [2 a[2] - 1] For the domain, {a[1] = 2, 2 <= a[2], a[3] = 0, a[4] = 0} The value of the game = , [{f[7](2, a[2] - 1, 1, 0)}, {f[9](2, a[2], 0) + [0]}] = , [{[{[2 a[2]]}, {[2 a[2]]}]}, {[{[{[2 a[2] - 1]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}] = , [2 a[2]] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, a[1] = 3} The value of the game = , [{f[7](3, a[2] - 1, 1, 0)}, {f[9](3, a[2], 0) + [0]}] = , [{[{[2 a[2] + 1/2]}, {[2 a[2] + 1/2]}]}, {[{[{[2 a[2]]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}] = , [2 a[2] + 1/2] For the domain, {2 <= a[2], a[3] = 0, a[4] = 0, 4 <= a[1]} The value of the game = , [{f[7](a[1], a[2] - 1, 1, 0)}, {f[9](a[1], a[2], 0) + [0]}] = , [{[a[1] + 2 a[2] - 3]}, {[{[{[a[1] + 2 a[2] - 3]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}] = , [{[a[1] + 2 a[2] - 3]}, {[2 a[2] + 1]}] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [{f[6](0, 0, 2, 0), f[7](1, 0, 0, 1)}, {f[9](1, 0, 1) + [0]}] = , [{[{[0]}, {[0]}], [1]}, {[{[{[1]}, {[1]}]}, {[3]}]}] = , [{[1]}, {[1]}] For the domain, {a[3] = 1, a[2] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [ {f[7](a[1], 0, 0, 1), f[6](a[1] - 1, 0, 2, 0)}, {f[9](a[1], 0, 1) + [0]}] = , [{[a[1]]}, {[{[{[a[1]]}, {[a[1]]}]}, {[3]}]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[7](0, 0, 0, 1)}, {f[9](0, 0, 1) + [0]}] = , [{[0]}, {[{[{[0]}, {[0]}]}, {[3]}]}] = , [{[0]}, {[0]}] For the domain, {a[3] = 1, a[1] = 0, a[4] = 0, 1 <= a[2]} The value of the game = , [ {f[7](0, a[2], 0, 1), f[7](0, a[2] - 1, 2, 0)}, {f[9](0, a[2], 1) + [0]}] = , [{[%1, %1], [%1, {[2 a[2] + 3]}]}, {[%1, {[2 a[2] + 3]}]}] %1 := {[2 a[2] - 1]} = , [{[2 a[2]]}, {[2 a[2]]}] For the domain, {a[3] = 1, a[4] = 0, a[1] = 1, 1 <= a[2]} The value of the game = , [ {f[7](1, a[2] - 1, 2, 0), f[7](1, a[2], 0, 1)}, {f[9](1, a[2], 1) + [0]}] = , [{[{[2 a[2]]}, {[2 a[2]]}], [{[2 a[2]]}, {[2 a[2] + 3]}]}, {[{[2 a[2]]}, {[2 a[2] + 3]}]}] = , [{[2 a[2] + 1]}, {[2 a[2] + 1]}] For the domain, {a[3] = 1, a[1] = 2, a[4] = 0, 1 <= a[2]} The value of the game = , [ {f[7](2, a[2] - 1, 2, 0), f[7](2, a[2], 0, 1)}, {f[9](2, a[2], 1) + [0]}] = , [{[%1, %1], [%1, {[2 a[2] + 3]}]}, {[%1, {[2 a[2] + 3]}]}] %1 := {[2 a[2] + 1]} = , [{[2 a[2] + 2]}, {[2 a[2] + 2]}] For the domain, {a[3] = 1, a[4] = 0, 1 <= a[2], a[1] = 3} The value of the game = , [ {f[7](3, a[2] - 1, 2, 0), f[7](3, a[2], 0, 1)}, {f[9](3, a[2], 1) + [0]}] = , [{[%1, %1], [%1, {[2 a[2] + 3]}]}, {[%1, {[2 a[2] + 3]}]}] %1 := {[2 a[2] + 2]} = , [{[2 a[2] + 5/2]}, {[2 a[2] + 5/2]}] For the domain, {a[3] = 1, a[4] = 0, 1 <= a[2], 4 <= a[1]} The value of the game = , [ {f[7](a[1], a[2] - 1, 2, 0), f[7](a[1], a[2], 0, 1)}, {f[9](a[1], a[2], 1) + [0]}] = , [{[%1, %1], [%1, {[2 a[2] + 3]}]}, {[%1, {[2 a[2] + 3]}]}] %1 := {[a[1] + 2 a[2] - 1]} = , [a[1] + 2 a[2] - 1] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, a[1] = 1} The value of the game = , [ {f[7](1, 0, a[3] - 1, 1), f[6](0, 0, a[3] + 1, 0)}, {f[9](1, 0, a[3]) + [0]}] = , [{[{[a[3] - 1]}, {[a[3] - 1]}], [a[3]]}, {[a[3]]}] = , [{[a[3]]}, {[a[3]]}] For the domain, {2 <= a[3], a[2] = 0, a[4] = 0, 2 <= a[1]} The value of the game = , [ {f[6](a[1] - 1, 0, a[3] + 1, 0), f[7](a[1], 0, a[3] - 1, 1)}, {f[9](a[1], 0, a[3]) + [0]}] = , [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{f[7](0, 0, a[3] - 1, 1)}, {f[9](0, 0, a[3]) + [0]}] = , [{[a[3] - 1]}, {[a[3] - 1]}] For the domain, {2 <= a[3], a[4] = 0, 0 <= a[1], 1 <= a[2]} The value of the game = , [{f[7](a[1], a[2] - 1, a[3] + 1, 0), f[7](a[1], a[2], a[3] - 1, 1)}, {f[9](a[1], a[2], a[3]) + [0]}] = , [{[a[1] + 2 a[2] + a[3] - 1], [{[a[1] + 2 a[2] - 2 + a[3]]}, {[a[1] + 2 a[2] - 2 + a[3]]}]} , {[a[1] + 2 a[2] + a[3] - 1]}] = , [{[a[1] + 2 a[2] + a[3] - 1]}, {[a[1] + 2 a[2] + a[3] - 1]}] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [ {f[6](0, 0, 1, 1), f[4](1, 0, 0, 0, 0) + [0]}, {f[9](1, 0, 0) + [2]}] = , [{[0], [{[-1]}, {[-1]}]}, {[3/2]}] = , [1] For the domain, {a[4] = 1, a[2] = 0, a[3] = 0, 2 <= a[1]} The value of the game = , [ {f[6](a[1] - 1, 0, 1, 1), f[4](a[1], 0, 0, 0, 0) + [0]}, {f[9](a[1], 0, 0) + [2]}] = , [{[a[1] - 1/2], [a[1] - 1]}, {[{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[2]}]}] = , [a[1]] For the domain, {a[4] = 1, a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{f[4](0, 0, 0, 0, 0) + [0]}, {f[9](0, 0, 0) + [2]}] = , [{[-3]}, {[1]}] = , [0] For the domain, {a[4] = 1, a[3] = 0, a[2] = 1, 0 <= a[1]} The value of the game = , [ {f[7](a[1], 0, 1, 1), f[4](a[1], 1, 0, 0, 0) + [0]}, {f[9](a[1], 1, 0) + [2]}] = , [{[1 + a[1]], [{[a[1]]}, {[a[1]]}]}, {[{[{[{[a[1] + 2]}, {[a[1] + 2]}]}, {[5]}]}, {[4]}]}] = , [{[1 + a[1]]}, {[5]}] For the domain, {a[4] = 1, 2 <= a[2], a[1] = 0, a[3] = 0} The value of the game = , [ {f[7](0, a[2] - 1, 1, 1), f[4](0, a[2], 0, 0, 0) + [0]}, {f[9](0, a[2], 0) + [2]}] = , [{[{[2 a[2] - 2]}, {[2 a[2] - 2]}], [2 a[2] - 1]}, {[{[{[2 a[2] - 1]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]}] = , [2 a[2]] For the domain, {a[4] = 1, 2 <= a[2], a[3] = 0, a[1] = 1} The value of the game = , [ {f[7](1, a[2] - 1, 1, 1), f[4](1, a[2], 0, 0, 0) + [0]}, {f[9](1, a[2], 0) + [2]}] = , [{[{[2 a[2] - 1]}, {[2 a[2] - 1]}], [2 a[2]]}, {[{[{[2 a[2]]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]}] = , [2 a[2] + 1] For the domain, {a[4] = 1, a[1] = 2, 2 <= a[2], a[3] = 0} The value of the game = , [ {f[7](2, a[2] - 1, 1, 1), f[4](2, a[2], 0, 0, 0) + [0]}, {f[9](2, a[2], 0) + [2]}] = , [{[{[2 a[2]]}, {[2 a[2]]}], [2 a[2] + 1]}, {[{[{[2 a[2] + 1]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]}] = , [2 a[2] + 2] For the domain, {a[4] = 1, 2 <= a[2], a[3] = 0, a[1] = 3} The value of the game = , [ {f[7](3, a[2] - 1, 1, 1), f[4](3, a[2], 0, 0, 0) + [0]}, {f[9](3, a[2], 0) + [2]}] = , [{[{[2 a[2] + 1/2]}, {[2 a[2] + 1/2]}], [2 a[2] + 2]}, {[{[{[2 a[2] + 2]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]}] = , [2 a[2] + 5/2] For the domain, {a[4] = 1, 2 <= a[2], a[3] = 0, 4 <= a[1]} The value of the game = , [ {f[7](a[1], a[2] - 1, 1, 1), f[4](a[1], a[2], 0, 0, 0) + [0]} , {f[9](a[1], a[2], 0) + [2]}] = , [{[a[1] + 2 a[2] - 3], [a[1] + 2 a[2] - 1]}, {[{[{[a[1] + 2 a[2] - 1]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]} ] = , [{[a[1] + 2 a[2] - 1]}, {[2 a[2] + 3]}] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[1] = 1} The value of the game = , [{ f[7](1, 0, 0, 2), f[4](1, 0, 1, 0, 0) + [0], f[6](0, 0, 2, 1) }, {f[9](1, 0, 1) + [2]}] = , [{[1]}, {[{[{[3]}, {[3]}]}, {[5]}]}] = , [2] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[1] = 1} The value of the game = , [{f[4](1, 0, a[3], 0, 0) + [0], f[7](1, 0, a[3] - 1, 2), f[6](0, 0, a[3] + 1, 1)}, {f[9](1, 0, a[3]) + [2]}] = , [{[a[3]]}, {[2 + a[3]]}] = , [a[3] + 1] For the domain, {a[3] = 1, a[4] = 1, a[1] = 2, a[2] = 0} The value of the game = , [{ f[4](2, 0, 1, 0, 0) + [0], f[6](1, 0, 2, 1), f[7](2, 0, 0, 2) }, {f[9](2, 0, 1) + [2]}] = , [{[2], [5/2]}, {[{[{[4]}, {[4]}]}, {[5]}]}] = , [3] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 2, a[2] = 0} The value of the game = , [{f[4](2, 0, a[3], 0, 0) + [0], f[6](1, 0, a[3] + 1, 1), f[7](2, 0, a[3] - 1, 2)}, {f[9](2, 0, a[3]) + [2]}] = , [{[3/2 + a[3]], [a[3] + 1]}, {[3 + a[3]]}] = , [2 + a[3]] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, a[1] = 3} The value of the game = , [{ f[6](2, 0, 2, 1), f[7](3, 0, 0, 2), f[4](3, 0, 1, 0, 0) + [0] }, {f[9](3, 0, 1) + [2]}] = , [{[3], [7/2]}, {[{[{[5]}, {[5]}]}, {[5]}]}] = , [4] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, a[1] = 3} The value of the game = , [{f[6](2, 0, a[3] + 1, 1), f[7](3, 0, a[3] - 1, 2), f[4](3, 0, a[3], 0, 0) + [0]}, {f[9](3, 0, a[3]) + [2]}] = , [{[2 + a[3]], [5/2 + a[3]]}, {[4 + a[3]]}] = , [3 + a[3]] For the domain, {a[3] = 1, a[4] = 1, a[2] = 0, 4 <= a[1]} The value of the game = , [{f[6](a[1] - 1, 0, 2, 1), f[4](a[1], 0, 1, 0, 0) + [0], f[7](a[1], 0, 0, 2)}, {f[9](a[1], 0, 1) + [2]}] = , [{[a[1]], [a[1] + 1/2]}, {[{[{[a[1] + 2]}, {[a[1] + 2]}]}, {[5]}]}] = , [1 + a[1]] For the domain, {a[4] = 1, 2 <= a[3], a[2] = 0, 4 <= a[1]} The value of the game = , [{f[6](a[1] - 1, 0, a[3] + 1, 1), f[7](a[1], 0, a[3] - 1, 2), f[4](a[1], 0, a[3], 0, 0) + [0]}, {f[9](a[1], 0, a[3]) + [2]}] = , [{[a[1] - 1/2 + a[3]], [a[1] + a[3] - 1]}, {[a[1] + 1 + a[3]]} ] = , [a[1] + a[3]] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, a[2] = 0} The value of the game = , [ {f[7](0, 0, 0, 2), f[4](0, 0, 1, 0, 0) + [0]}, {f[9](0, 0, 1) + [2]}] = , [{[0]}, {[{[{[2]}, {[2]}]}, {[5]}]}] = , [1] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, a[2] = 0} The value of the game = , [ {f[4](0, 0, a[3], 0, 0) + [0], f[7](0, 0, a[3] - 1, 2)}, {f[9](0, 0, a[3]) + [2]}] = , [{[a[3] - 1]}, {[a[3] + 1]}] = , [a[3]] For the domain, {a[3] = 1, a[4] = 1, a[1] = 0, 1 <= a[2]} The value of the game = , [{f[7](0, a[2] - 1, 2, 1), f[7](0, a[2], 0, 2), f[4](0, a[2], 1, 0, 0) + [0]}, {f[9](0, a[2], 1) + [2]}] = , [{[2 a[2]]}, {[{[2 a[2] + 1]}, {[2 a[2] + 5]}]}] = , [2 a[2] + 1] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2], a[3], 0, 0) + [0], f[7](0, a[2] - 1, a[3] + 1, 1), f[7](0, a[2], a[3] - 1, 2)}, {f[9](0, a[2], a[3]) + [2]}] = , [{[2 a[2] + a[3] - 1]}, {[2 a[2] + a[3] + 1]}] = , [2 a[2] + a[3]] For the domain, {a[3] = 1, a[4] = 1, a[1] = 1, 1 <= a[2]} The value of the game = , [{f[4](1, a[2], 1, 0, 0) + [0], f[7](1, a[2] - 1, 2, 1), f[7](1, a[2], 0, 2)}, {f[9](1, a[2], 1) + [2]}] = , [{[2 a[2] + 1]}, {[{[2 a[2] + 2]}, {[2 a[2] + 5]}]}] = , [2 a[2] + 2] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 1, 1 <= a[2]} The value of the game = , [{f[7](1, a[2], a[3] - 1, 2), f[7](1, a[2] - 1, a[3] + 1, 1), f[4](1, a[2], a[3], 0, 0) + [0]}, {f[9](1, a[2], a[3]) + [2]} ] = , [{[2 a[2] + a[3]]}, {[2 a[2] + a[3] + 2]}] = , [2 a[2] + a[3] + 1] For the domain, {a[3] = 1, a[4] = 1, a[1] = 2, 1 <= a[2]} The value of the game = , [{f[7](2, a[2], 0, 2), f[4](2, a[2], 1, 0, 0) + [0], f[7](2, a[2] - 1, 2, 1)}, {f[9](2, a[2], 1) + [2]}] = , [{[2 a[2] + 2]}, {[{[2 a[2] + 3]}, {[2 a[2] + 5]}]}] = , [2 a[2] + 3] For the domain, {a[4] = 1, 2 <= a[3], a[1] = 2, 1 <= a[2]} The value of the game = , [{f[7](2, a[2] - 1, a[3] + 1, 1), f[7](2, a[2], a[3] - 1, 2), f[4](2, a[2], a[3], 0, 0) + [0]}, {f[9](2, a[2], a[3]) + [2]}] = , [{[2 a[2] + a[3] + 1]}, {[2 a[2] + a[3] + 3]}] = , [2 a[2] + a[3] + 2] For the domain, {a[3] = 1, a[4] = 1, 1 <= a[2], a[1] = 3} The value of the game = , [{f[7](3, a[2] - 1, 2, 1), f[7](3, a[2], 0, 2), f[4](3, a[2], 1, 0, 0) + [0]}, {f[9](3, a[2], 1) + [2]}] = , [{[2 a[2] + 5/2], [2 a[2] + 3]}, {[{[2 a[2] + 4]}, {[2 a[2] + 5]}]}] = , [2 a[2] + 4] For the domain, {a[4] = 1, 2 <= a[3], 1 <= a[2], a[1] = 3} The value of the game = , [{f[4](3, a[2], a[3], 0, 0) + [0], f[7](3, a[2], a[3] - 1, 2), f[7](3, a[2] - 1, a[3] + 1, 1)}, {f[9](3, a[2], a[3]) + [2]}] = , [{[2 a[2] + a[3] + 2]}, {[2 a[2] + a[3] + 4]}] = , [2 a[2] + a[3] + 3] For the domain, {a[3] = 1, a[4] = 1, 1 <= a[2], 4 <= a[1]} The value of the game = , [{f[7](a[1], a[2] - 1, 2, 1), f[4](a[1], a[2], 1, 0, 0) + [0], f[7](a[1], a[2], 0, 2)}, {f[9](a[1], a[2], 1) + [2]}] = , [{[{[a[1] + 2 a[2] - 1]}, {[a[1] + 2 a[2] - 1]}], [a[1] + 2 a[2]]}, {[{[a[1] + 2 a[2] + 1]}, {[2 a[2] + 5]}]}] = , [a[1] + 2 a[2] + 1] For the domain, {a[4] = 1, 2 <= a[3], 1 <= a[2], 4 <= a[1]} The value of the game = , [{f[4](a[1], a[2], a[3], 0, 0) + [0], f[7](a[1], a[2] - 1, a[3] + 1, 1), f[7](a[1], a[2], a[3] - 1, 2)}, {f[9](a[1], a[2], a[3]) + [2]}] = , [{[a[1] + 2 a[2] + a[3] - 1]}, {[a[1] + 2 a[2] + a[3] + 1]}] = , [a[1] + 2 a[2] + a[3]] For the domain, {a[3] = 1, a[2] = 0, a[1] = 1, a[4] = 2} The value of the game = , [{ f[4](1, 0, 1, 1, 0) + [0], f[6](0, 0, 2, 2), f[7](1, 0, 0, 3) }, {}] = , [{[1], [{[2]}, {[2]}]}, {}] = , [2] For the domain, {2 <= a[3], a[2] = 0, a[1] = 1, a[4] = 2} The value of the game = , [{f[4](1, 0, a[3], 1, 0) + [0], f[6](0, 0, a[3] + 1, 2), f[7](1, 0, a[3] - 1, 3)}, {}] = , [{[a[3]], [{[a[3] + 1]}, {[a[3] + 1]}]}, {}] = , [a[3] + 1] For the domain, {a[2] = 0, a[1] = 1, 1 <= a[3], a[4] = 3} The value of the game = , [{f[6](0, 0, a[3] + 1, 3), f[7](1, 0, a[3] - 1, 4), f[4](1, 0, a[3], 2, 0) + [0]}, {}] = , [{[a[3]], [{[{[2 + 2 a[3]]}, {[2 + a[3]]}]}, {[a[3] + 1]}]}, {}] = , [a[3] + 1] For the domain, {a[2] = 0, a[1] = 1, 1 <= a[3], 4 <= a[4]} The value of the game = , [{f[6](0, 0, a[3] + 1, a[4]), f[4](1, 0, a[3], a[4] - 1, 0) + [0], f[7](1, 0, a[3] - 1, a[4] + 1)}, {}] = , [{[a[3]], [{[{[-1 + 2 a[3] + a[4]]}, {[2 + a[3]]}]}, {[a[3] + 1]}]}, {} ] = , [a[3] + 1] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1, a[4] = 2} The value of the game = , [{f[4](1, 0, 0, 1, 0) + [0], f[6](0, 0, 1, 2)}, {}] = , [{[0]}, {}] = , [1] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1, a[4] = 3} The value of the game = , [{f[6](0, 0, 1, 3), f[4](1, 0, 0, 2, 0) + [0]}, {}] = , [{[0], [{[{[2]}, {[2]}]}, {[1]}]}, {}] = , [1] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1, 4 <= a[4]} The value of the game = , [{f[6](0, 0, 1, a[4]), f[4](1, 0, 0, a[4] - 1, 0) + [0]}, {}] = , [{[0], [{[{[a[4] - 1]}, {[2]}]}, {[1]}]}, {}] = , [1] For the domain, {a[3] = 1, a[1] = 2, a[2] = 0, a[4] = 2} The value of the game = , [{ f[7](2, 0, 0, 3), f[6](1, 0, 2, 2), f[4](2, 0, 1, 1, 0) + [0] }, {}] = , [{[2], [5/2], [{[3]}, {[3]}]}, {}] = , [3] For the domain, {a[3] = 1, a[2] = 0, a[4] = 2, a[1] = 3} The value of the game = , [{ f[6](2, 0, 2, 2), f[7](3, 0, 0, 3), f[4](3, 0, 1, 1, 0) + [0] }, {}] = , [{[3], [7/2], [{[4]}, {[4]}]}, {}] = , [4] For the domain, {a[3] = 1, a[2] = 0, a[4] = 2, 4 <= a[1]} The value of the game = , [{f[6](a[1] - 1, 0, 2, 2), f[7](a[1], 0, 0, 3), f[4](a[1], 0, 1, 1, 0) + [0]}, {}] = , [{[a[1]], [a[1] + 1/2], [{[1 + a[1]]}, {[1 + a[1]]}]}, {}] = , [1 + a[1]] For the domain, {2 <= a[3], a[2] = 0, 2 <= a[1], a[4] = 2} The value of the game = , [{f[6](a[1] - 1, 0, a[3] + 1, 2), f[7](a[1], 0, a[3] - 1, 3), f[4](a[1], 0, a[3], 1, 0) + [0]}, {}] = , [{[a[1] - 1/2 + a[3]], [a[1] + a[3] - 1], [{[a[1] + a[3]]}, {[a[1] + a[3]]}]}, {}] = , [a[1] + a[3]] For the domain, {a[1] = 2, a[2] = 0, 1 <= a[3], a[4] = 3} The value of the game = , [{f[4](2, 0, a[3], 2, 0) + [0], f[7](2, 0, a[3] - 1, 4), f[6](1, 0, a[3] + 1, 3)}, {}] = , [{[3/2 + a[3]], [a[3] + 1], [{[{[4 + 2 a[3]]}, {[3 + a[3]]}]}, {[2 + a[3]]}]}, {}] = , [2 + a[3]] For the domain, {a[2] = 0, 1 <= a[3], a[1] = 3, a[4] = 3} The value of the game = , [{f[4](3, 0, a[3], 2, 0) + [0], f[6](2, 0, a[3] + 1, 3), f[7](3, 0, a[3] - 1, 4)}, {}] = , [{[5/2 + a[3]], [{[{[6 + 2 a[3]]}, {[4 + a[3]]}]}, {[3 + a[3]]}], [2 + a[3]]} , {}] = , [3 + a[3]] For the domain, {a[2] = 0, 1 <= a[3], 4 <= a[1], a[4] = 3} The value of the game = , [{f[6](a[1] - 1, 0, a[3] + 1, 3), f[7](a[1], 0, a[3] - 1, 4), f[4](a[1], 0, a[3], 2, 0) + [0]}, {}] = , [{[ {[{[2 a[1] + 2 a[3]]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]} ], [a[1] - 1/2 + a[3]], [a[1] + a[3] - 1]}, {}] = , [a[1] + a[3]] For the domain, {a[2] = 0, 2 <= a[1], 1 <= a[3], 4 <= a[4]} The value of the game = , [{f[6](a[1] - 1, 0, a[3] + 1, a[4]), f[7](a[1], 0, a[3] - 1, a[4] + 1), f[4](a[1], 0, a[3], a[4] - 1, 0) + [0]}, {}] = , [{[a[1] - 1/2 + a[3]], [a[1] + a[3] - 1], [ {[{[2 a[1] + 2 a[3] + a[4] - 3]}, {[a[1] + 1 + a[3]]}]}, {[a[1] + a[3]]}]}, {}] = , [a[1] + a[3]] For the domain, {a[2] = 0, a[3] = 0, 2 <= a[1], a[4] = 2} The value of the game = , [{f[6](a[1] - 1, 0, 1, 2), f[4](a[1], 0, 0, 1, 0) + [0]}, {}] = , [{[a[1] - 1/2], [{[a[1]]}, {[a[1]]}]}, {}] = , [a[1]] For the domain, {a[1] = 2, a[2] = 0, a[3] = 0, a[4] = 3} The value of the game = , [{f[4](2, 0, 0, 2, 0) + [0], f[6](1, 0, 1, 3)}, {}] = , [{[3/2], [{[{[4]}, {[3]}]}, {[2]}]}, {}] = , [2] For the domain, {a[2] = 0, a[3] = 0, a[1] = 3, a[4] = 3} The value of the game = , [{f[6](2, 0, 1, 3), f[4](3, 0, 0, 2, 0) + [0]}, {}] = , [{[5/2], [{[{[6]}, {[4]}]}, {[3]}]}, {}] = , [3] For the domain, {a[2] = 0, a[3] = 0, 4 <= a[1], a[4] = 3} The value of the game = , [{f[4](a[1], 0, 0, 2, 0) + [0], f[6](a[1] - 1, 0, 1, 3)}, {}] = , [{[a[1] - 1/2], [{[{[2 a[1]]}, {[1 + a[1]]}]}, {[a[1]]}]}, {}] = , [a[1]] For the domain, {a[2] = 0, a[3] = 0, 2 <= a[1], 4 <= a[4]} The value of the game = , [{f[6](a[1] - 1, 0, 1, a[4]), f[4](a[1], 0, 0, a[4] - 1, 0) + [0]}, {}] = , [{[a[1] - 1/2], [{[{[2 a[1] + a[4] - 3]}, {[1 + a[1]]}]}, {[a[1]]}]}, {}] = , [a[1]] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0, a[4] = 2} The value of the game = , [{f[7](0, 0, 0, 3), f[4](0, 0, 1, 1, 0) + [0]}, {}] = , [{[0], [{[1]}, {[1]}]}, {}] = , [1] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0, a[4] = 2} The value of the game = , [{f[7](0, 0, a[3] - 1, 3), f[4](0, 0, a[3], 1, 0) + [0]}, {}] = , [{[a[3] - 1], [{[a[3]]}, {[a[3]]}]}, {}] = , [a[3]] For the domain, {a[1] = 0, a[2] = 0, 1 <= a[3], a[4] = 3} The value of the game = , [{f[7](0, 0, a[3] - 1, 4), f[4](0, 0, a[3], 2, 0) + [0]}, {}] = , [{[{[{[2 a[3]]}, {[a[3] + 1]}]}, {[a[3]]}], [a[3] - 1]}, {}] = , [a[3]] For the domain, {a[1] = 0, a[2] = 0, 1 <= a[3], 4 <= a[4]} The value of the game = , [{f[7](0, 0, a[3] - 1, a[4] + 1), f[4](0, 0, a[3], a[4] - 1, 0) + [0]}, {}] = , [{[a[3] - 1], [{[{[2 a[3] + a[4] - 3]}, {[a[3] + 1]}]}, {[a[3]]}]}, {}] = , [a[3]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 2} The value of the game = , [{f[4](0, 0, 0, 1, 0) + [0]}, {}] = , [{[-1]}, {}] = , [0] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, a[4] = 3} The value of the game = , [{f[4](0, 0, 0, 2, 0) + [0]}, {}] = , [{[{[{[0]}, {[1]}]}, {[0]}]}, {}] = , [0] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0, 4 <= a[4]} The value of the game = , [{f[4](0, 0, 0, a[4] - 1, 0) + [0]}, {}] = , [{[{[{[a[4] - 3]}, {[1]}]}, {[0]}]}, {}] = , [0] For the domain, {a[3] = 1, a[1] = 0, 1 <= a[2], a[4] = 2} The value of the game = , [{f[4](0, a[2], 1, 1, 0) + [0], f[7](0, a[2], 0, 3), f[7](0, a[2] - 1, 2, 2)}, {}] = , [{[2 a[2]], [{[2 a[2] + 1]}, {[2 a[2] + 1]}]}, {}] = , [2 a[2] + 1] For the domain, {a[3] = 1, a[1] = 1, 1 <= a[2], a[4] = 2} The value of the game = , [{f[4](1, a[2], 1, 1, 0) + [0], f[7](1, a[2], 0, 3), f[7](1, a[2] - 1, 2, 2)}, {}] = , [{[2 a[2] + 1], [{[2 a[2] + 2]}, {[2 a[2] + 2]}]}, {}] = , [2 a[2] + 2] For the domain, {a[3] = 1, a[1] = 2, 1 <= a[2], a[4] = 2} The value of the game = , [{f[7](2, a[2], 0, 3), f[7](2, a[2] - 1, 2, 2), f[4](2, a[2], 1, 1, 0) + [0]}, {}] = , [{[2 a[2] + 2], [{[2 a[2] + 3]}, {[2 a[2] + 3]}]}, {}] = , [2 a[2] + 3] For the domain, {a[3] = 1, 1 <= a[2], a[4] = 2, a[1] = 3} The value of the game = , [{f[7](3, a[2], 0, 3), f[7](3, a[2] - 1, 2, 2), f[4](3, a[2], 1, 1, 0) + [0]}, {}] = , [{[2 a[2] + 3], [2 a[2] + 15/4]}, {}] = , [2 a[2] + 4] For the domain, {a[3] = 1, 1 <= a[2], a[4] = 2, 4 <= a[1]} The value of the game = , [{f[7](a[1], a[2], 0, 3), f[7](a[1], a[2] - 1, 2, 2), f[4](a[1], a[2], 1, 1, 0) + [0]}, {}] = , [{[a[1] + 2 a[2]]}, {}] = , [a[1] + 2 a[2] + 1] For the domain, {2 <= a[3], 0 <= a[1], 1 <= a[2], a[4] = 2} The value of the game = , [{f[7](a[1], a[2] - 1, a[3] + 1, 2), f[7](a[1], a[2], a[3] - 1, 3), f[4](a[1], a[2], a[3], 1, 0) + [0]}, {}] = , [{[a[1] + 2 a[2] + a[3] - 1], [{[a[1] + 2 a[2] + a[3]]}, {[a[1] + 2 a[2] + a[3]]}]}, {}] = , [a[1] + 2 a[2] + a[3]] For the domain, {a[1] = 0, 1 <= a[2], 1 <= a[3], a[4] = 3} The value of the game = , [{f[4](0, a[2], a[3], 2, 0) + [0], f[7](0, a[2] - 1, a[3] + 1, 3), f[7](0, a[2], a[3] - 1, 4)}, {}] = , [{[2 a[2] + a[3] - 1], [ {[{[3 a[2] + 2 a[3]]}, {[2 a[2] + a[3] + 1]}]}, {[2 a[2] + a[3]]}]}, {}] = , [2 a[2] + a[3]] For the domain, {a[1] = 1, 1 <= a[2], 1 <= a[3], a[4] = 3} The value of the game = , [{f[4](1, a[2], a[3], 2, 0) + [0], f[7](1, a[2], a[3] - 1, 4), f[7](1, a[2] - 1, a[3] + 1, 3)}, {}] = , [{[2 a[2] + a[3]], [ {[{[3 a[2] + 2 a[3] + 2]}, {[2 a[2] + a[3] + 2]}]}, {[2 a[2] + a[3] + 1]}]}, {}] = , [2 a[2] + a[3] + 1] For the domain, {a[1] = 2, 1 <= a[2], 1 <= a[3], a[4] = 3} The value of the game = , [{f[7](2, a[2], a[3] - 1, 4), f[7](2, a[2] - 1, a[3] + 1, 3), f[4](2, a[2], a[3], 2, 0) + [0]}, {}] = , [{[2 a[2] + a[3] + 1], [ {[{[3 a[2] + 2 a[3] + 4]}, {[2 a[2] + a[3] + 3]}]}, {[2 a[2] + a[3] + 2]}]}, {}] = , [2 a[2] + a[3] + 2] For the domain, {1 <= a[2], 1 <= a[3], a[1] = 3, a[4] = 3} The value of the game = , [{f[7](3, a[2], a[3] - 1, 4), f[7](3, a[2] - 1, a[3] + 1, 3), f[4](3, a[2], a[3], 2, 0) + [0]}, {}] = , [{[2 a[2] + a[3] + 2], [ {[{[3 a[2] + 2 a[3] + 6]}, {[2 a[2] + a[3] + 4]}]}, {[2 a[2] + a[3] + 3]}]}, {}] = , [2 a[2] + a[3] + 3] For the domain, {1 <= a[2], 1 <= a[3], 4 <= a[1], a[4] = 3} The value of the game = , [{f[4](a[1], a[2], a[3], 2, 0) + [0], f[7](a[1], a[2], a[3] - 1, 4), f[7](a[1], a[2] - 1, a[3] + 1, 3)}, {}] = , [{[a[1] + 2 a[2] + a[3] - 1], [{ [{[2 a[1] + 3 a[2] + 2 a[3]]}, {[a[1] + 2 a[2] + a[3] + 1]}]} , {[a[1] + 2 a[2] + a[3]]}]}, {}] = , [a[1] + 2 a[2] + a[3]] For the domain, {0 <= a[1], 1 <= a[2], 1 <= a[3], 4 <= a[4]} The value of the game = , [{f[7](a[1], a[2] - 1, a[3] + 1, a[4]), f[4](a[1], a[2], a[3], a[4] - 1, 0) + [0], f[7](a[1], a[2], a[3] - 1, a[4] + 1)}, {}] = , [{[a[1] + 2 a[2] + a[3] - 1], [{[ {[2 a[1] + 3 a[2] + 2 a[3] + a[4] - 3]}, {[a[1] + 2 a[2] + a[3] + 1]}]}, {[a[1] + 2 a[2] + a[3]]}]}, {}] = , [a[1] + 2 a[2] + a[3]] For the domain, {a[3] = 0, 0 <= a[1], 1 <= a[2], a[4] = 2} The value of the game = , [ {f[4](a[1], a[2], 0, 1, 0) + [0], f[7](a[1], a[2] - 1, 1, 2)} , {}] = , [{[a[1] + 2 a[2] - 1]}, {}] = , [a[1] + 2 a[2]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 3} The value of the game = , [{f[4](0, a[2], 0, 2, 0) + [0], f[7](0, a[2] - 1, 1, 3)}, {}] = , [{[2 a[2] - 1], [{[{[3 a[2]]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}, {}] = , [2 a[2]] For the domain, {a[3] = 0, a[1] = 1, 1 <= a[2], a[4] = 3} The value of the game = , [{f[4](1, a[2], 0, 2, 0) + [0], f[7](1, a[2] - 1, 1, 3)}, {}] = , [{[2 a[2]], [{[{[3 a[2] + 2]}, {[2 a[2] + 2]}]}, {[2 a[2] + 1]}]}, {}] = , [2 a[2] + 1] For the domain, {a[1] = 2, a[3] = 0, 1 <= a[2], a[4] = 3} The value of the game = , [{f[4](2, a[2], 0, 2, 0) + [0], f[7](2, a[2] - 1, 1, 3)}, {}] = , [{[2 a[2] + 1], [{[{[3 a[2] + 4]}, {[2 a[2] + 3]}]}, {[2 a[2] + 2]}]}, {}] = , [2 a[2] + 2] For the domain, {a[3] = 0, 1 <= a[2], a[1] = 3, a[4] = 3} The value of the game = , [{f[7](3, a[2] - 1, 1, 3), f[4](3, a[2], 0, 2, 0) + [0]}, {}] = , [{[2 a[2] + 2], [{[{[3 a[2] + 6]}, {[2 a[2] + 7/2]}]}, {[2 a[2] + 3]}]}, {}] = , [2 a[2] + 3] For the domain, {a[3] = 0, 1 <= a[2], 4 <= a[1], a[4] = 3} The value of the game = , [ {f[4](a[1], a[2], 0, 2, 0) + [0], f[7](a[1], a[2] - 1, 1, 3)} , {}] = , [{[a[1] + 2 a[2] - 1], [{[a[1] + 2 a[2]]}, {[a[1] + 2 a[2]]}]} , {}] = , [a[1] + 2 a[2]] For the domain, {a[3] = 0, 0 <= a[1], 1 <= a[2], 4 <= a[4]} The value of the game = , [{f[4](a[1], a[2], 0, a[4] - 1, 0) + [0], f[7](a[1], a[2] - 1, 1, a[4])}, {}] = , [{[a[1] + 2 a[2] - 1], [ {[{[2 a[1] + 3 a[2] - 3 + a[4]]}, {[a[1] + 2 a[2] + 1]}]}, {[a[1] + 2 a[2]]}]}, {}] = , [a[1] + 2 a[2]] ########## #, f[8], # ########## For the domain, {a[3] = 1, a[1] = 0, a[2] = 0} The value of the game = , [{f[6](0, 0, 0, 0) + [1]}, {f[9](0, 0, 1)}] = , [{[-2]}, {[{[{[0]}, {[0]}]}, {[3]}]}] = , [-1] For the domain, {2 <= a[3], a[1] = 0, a[2] = 0} The value of the game = , [{f[6](0, 0, a[3] - 1, 0) + [1]}, {f[9](0, 0, a[3])}] = , [{[{[a[3] - 2]}, {[a[3] - 2]}]}, {[a[3] - 1]}] = , [a[3] - 2] For the domain, {a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{}, {f[9](0, 0, 0)}] = , [{}, {[-1]}] = , [-2] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [{f[8](0, 1, 0)}, {f[9](1, 0, 0)}] = , [{[{[-1]}, {[3]}]}, {[-1/2]}] = , [{[0]}, {[-1/2]}] For the domain, {a[1] = 2, a[2] = 0, a[3] = 0} The value of the game = , [{f[8](1, 1, 0)}, {f[9](2, 0, 0)}] = , [{[{[0]}, {[3]}]}, {[{[{[1]}, {[1]}]}, {[0]}]}] = , [{[1]}, {[1]}] For the domain, {a[2] = 0, a[3] = 0, a[1] = 3} The value of the game = , [{f[8](2, 1, 0)}, {f[9](3, 0, 0)}] = , [{[{[1]}, {[3]}]}, {[{[{[2]}, {[2]}]}, {[0]}]}] = , [{[2]}, {[2]}] For the domain, {a[2] = 0, a[3] = 0, a[1] = 4} The value of the game = , [{f[8](3, 1, 0)}, {f[9](4, 0, 0)}] = , [{[{[2]}, {[3]}]}, {[{[{[3]}, {[3]}]}, {[0]}]}] = , [11/4] For the domain, {a[2] = 0, a[3] = 0, 5 <= a[1]} The value of the game = , [{f[8](a[1] - 1, 1, 0)}, {f[9](a[1], 0, 0)}] = , [{[{[a[1] - 2]}, {[3]}]}, {[{[{[a[1] - 1]}, {[a[1] - 1]}]}, {[0]}]}] = , [3] For the domain, {a[3] = 1, a[2] = 0, a[1] = 1} The value of the game = , [{f[6](1, 0, 0, 0) + [1], f[8](0, 1, 1)}, {f[9](1, 0, 1)}] = , [{[{[0]}, {[0]}], [1]}, {[{[{[1]}, {[1]}]}, {[3]}]}] = , [{[1]}, {[1]}] For the domain, {a[3] = 1, a[2] = 0, 2 <= a[1]} The value of the game = , [ {f[8](a[1] - 1, 1, 1), f[6](a[1], 0, 0, 0) + [1]}, {f[9](a[1], 0, 1)}] = , [{[a[1]], [{[a[1] - 1]}, {[4]}]}, {[{[{[a[1]]}, {[a[1]]}]}, {[3]}]}] = , [{[a[1]]}, {[a[1]]}] For the domain, {2 <= a[3], a[2] = 0, 1 <= a[1]} The value of the game = , [ {f[8](a[1] - 1, 1, a[3]), f[6](a[1], 0, a[3] - 1, 0) + [1]}, {f[9](a[1], 0, a[3])}] = , [{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}] For the domain, {a[3] = 0, a[2] = 1, 1 <= a[1]} The value of the game = , [{f[8](a[1] - 1, 2, 0)}, {f[9](a[1], 1, 0)}] = , [{[a[1] - 1]}, {[{[{[{[a[1]]}, {[a[1]]}]}, {[3]}]}, {[2]}]}] = , [{[a[1] - 1]}, {[3]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 1} The value of the game = , [{}, {f[9](0, 1, 0)}] = , [{}, {[{[{[{[0]}, {[0]}]}, {[3]}]}, {[2]}]}] = , [0] For the domain, {a[3] = 1, a[2] = 1, 1 <= a[1]} The value of the game = , [ {f[6](a[1], 1, 0, 0) + [1], f[8](a[1] - 1, 2, 1)}, {f[9](a[1], 1, 1)}] = , [{[a[1]], [{[a[1]]}, {[{[a[1]]}, {[4]}]}]}, {[{[1 + a[1]]}, {[5]}]}] = , [1 + a[1]] For the domain, {2 <= a[3], a[2] = 1, 1 <= a[1]} The value of the game = , [ {f[8](a[1] - 1, 2, a[3]), f[6](a[1], 1, a[3] - 1, 0) + [1]}, {f[9](a[1], 1, a[3])}] = , [{[a[1] - 1/2 + a[3]], [a[1] + a[3] - 1]}, {[a[1] + 1 + a[3]]} ] = , [a[1] + a[3]] For the domain, {a[3] = 1, a[1] = 0, a[2] = 1} The value of the game = , [{f[6](0, 1, 0, 0) + [1]}, {f[9](0, 1, 1)}] = , [{[0]}, {[{[1]}, {[5]}]}] = , [1] For the domain, {2 <= a[3], a[1] = 0, a[2] = 1} The value of the game = , [{f[6](0, 1, a[3] - 1, 0) + [1]}, {f[9](0, 1, a[3])}] = , [{[- 1/2 + a[3]]}, {[a[3] + 1]}] = , [a[3]] For the domain, {a[3] = 1, 1 <= a[1], a[2] = 2} The value of the game = , [{f[8](a[1] - 1, 3, 1), f[6](a[1], 2, 0, 0) + [1]}, {}] = , [{[a[1]], [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[1 + a[1]]}]}, {}] = , [1 + a[1]] For the domain, {a[3] = 1, 3 <= a[2], 1 <= a[1]} The value of the game = , [ {f[8](a[1] - 1, a[2] + 1, 1), f[6](a[1], a[2], 0, 0) + [1]}, {}] = , [{[a[1]], [ {[{[{[2 a[1] + a[2] - 2]}, {[a[1] + 2]}]}, {[1 + a[1]]}]}, {[1 + a[1]]}]}, {}] = , [1 + a[1]] For the domain, {2 <= a[3], 2 <= a[2], 1 <= a[1]} The value of the game = , [{f[8](a[1] - 1, a[2] + 1, a[3]), f[6](a[1], a[2], a[3] - 1, 0) + [1]}, {}] = , [{[a[1] - 1/2 + a[3]], [a[1] + a[3] - 1]}, {}] = , [a[1] + a[3]] For the domain, {2 <= a[2], a[3] = 0, 1 <= a[1]} The value of the game = , [{f[8](a[1] - 1, a[2] + 1, 0)}, {}] = , [{[a[1] - 1]}, {}] = , [a[1]] For the domain, {a[3] = 1, a[1] = 0, a[2] = 2} The value of the game = , [{f[6](0, 2, 0, 0) + [1]}, {}] = , [{[3/4]}, {}] = , [1] For the domain, {a[3] = 1, 3 <= a[2], a[1] = 0} The value of the game = , [{f[6](0, a[2], 0, 0) + [1]}, {}] = , [{[{[{[{[-2 + a[2]]}, {[2]}]}, {[1]}]}, {[1]}]}, {}] = , [1] For the domain, {2 <= a[3], 2 <= a[2], a[1] = 0} The value of the game = , [{f[6](0, a[2], a[3] - 1, 0) + [1]}, {}] = , [{[- 1/2 + a[3]]}, {}] = , [a[3]] For the domain, {2 <= a[2], a[1] = 0, a[3] = 0} The value of the game = , [{}, {}] = , [{}, {}] = , [0] ########## #, f[9], # ########## For the domain, {a[1] = 0, a[2] = 0, a[3] = 0} The value of the game = , [{}, {f[10](0, 0) + [0]}] = , [{}, {[0]}] = , [-1] For the domain, {a[2] = 0, a[3] = 0, a[1] = 1} The value of the game = , [{f[8](0, 0, 1)}, {f[10](1, 0) + [0]}] = , [{[-1]}, {[0]}] = , [-1/2] For the domain, {a[2] = 0, a[3] = 0, 2 <= a[1]} The value of the game = , [{f[8](a[1] - 1, 0, 1)}, {f[10](a[1], 0) + [0]}] = , [{[{[a[1] - 1]}, {[a[1] - 1]}]}, {[0]}] For the domain, {a[3] = 0, a[2] = 1, 0 <= a[1]} The value of the game = , [{f[9](a[1], 0, 1)}, {f[10](a[1], 1) + [0]}] = , [{[{[{[a[1]]}, {[a[1]]}]}, {[3]}]}, {[2]}] For the domain, {2 <= a[2], a[3] = 0, 0 <= a[1]} The value of the game = , [{f[9](a[1], a[2] - 1, 1)}, {f[10](a[1], a[2]) + [0]}] = , [{[{[a[1] + 2 a[2] - 3]}, {[2 a[2] + 1]}]}, {[2 a[2]]}] For the domain, {a[3] = 1, a[2] = 0, a[1] = 1} The value of the game = , [ {f[7](1, 0, 0, 0) + [1], f[8](0, 0, 2)}, {f[10](1, 0) + [3]}] = , [{[0]}, {[3]}] = , [1] For the domain, {a[3] = 1, a[2] = 0, 2 <= a[1]} The value of the game = , [ {f[7](a[1], 0, 0, 0) + [1], f[8](a[1] - 1, 0, 2)}, {f[10](a[1], 0) + [3]}] = , [{[{[a[1]]}, {[a[1]]}]}, {[3]}] For the domain, {a[3] = 1, a[1] = 0, a[2] = 0} The value of the game = , [{f[7](0, 0, 0, 0) + [1]}, {f[10](0, 0) + [3]}] = , [{[-1]}, {[3]}] = , [0] For the domain, {a[3] = 1, a[2] = 1, 0 <= a[1]} The value of the game = , [ {f[7](a[1], 1, 0, 0) + [1], f[9](a[1], 0, 2)}, {f[10](a[1], 1) + [3]}] = , [{[1 + a[1]], [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[4]}]}, {[5]}] = , [{[1 + a[1]]}, {[5]}] For the domain, {a[3] = 1, 2 <= a[2], 0 <= a[1]} The value of the game = , [ {f[7](a[1], a[2], 0, 0) + [1], f[9](a[1], a[2] - 1, 2)}, {f[10](a[1], a[2]) + [3]}] = , [{[a[1] + 2 a[2] - 1], [{[a[1] + 2 a[2] - 2]}, {[2 a[2] + 2]}] }, {[2 a[2] + 3]}] = , [{[a[1] + 2 a[2] - 1]}, {[2 a[2] + 3]}] For the domain, {a[2] = 0, a[1] = 1, a[3] = 2} The value of the game = , [{f[8](0, 0, 3), f[7](1, 0, 1, 0) + [1]}, {}] = , [{[1], [{[2]}, {[2]}]}, {}] = , [2] For the domain, {3 <= a[3], a[2] = 0, a[1] = 1} The value of the game = , [{f[8](0, 0, a[3] + 1), f[7](1, 0, a[3] - 1, 0) + [1]}, {}] = , [{[a[3] - 1], [{[a[3]]}, {[a[3]]}]}, {}] = , [a[3]] For the domain, {a[2] = 0, 2 <= a[1], a[3] = 2} The value of the game = , [{f[7](a[1], 0, 1, 0) + [1], f[8](a[1] - 1, 0, 3)}, {}] = , [{[{[1 + a[1]]}, {[1 + a[1]]}]}, {}] = , [1 + a[1]] For the domain, {3 <= a[3], a[2] = 0, 2 <= a[1]} The value of the game = , [{ f[8](a[1] - 1, 0, a[3] + 1), f[7](a[1], 0, a[3] - 1, 0) + [1] }, {}] = , [{[{[a[1] + a[3] - 1]}, {[a[1] + a[3] - 1]}]}, {}] = , [a[1] + a[3] - 1] For the domain, {a[1] = 0, a[2] = 0, a[3] = 2} The value of the game = , [{f[7](0, 0, 1, 0) + [1]}, {}] = , [{[{[1]}, {[1]}]}, {}] = , [1] For the domain, {3 <= a[3], a[1] = 0, a[2] = 0} The value of the game = , [{f[7](0, 0, a[3] - 1, 0) + [1]}, {}] = , [{[{[a[3] - 1]}, {[a[3] - 1]}]}, {}] = , [a[3] - 1] For the domain, {a[1] = 0, a[3] = 2, 1 <= a[2]} The value of the game = , [{f[7](0, a[2], 1, 0) + [1], f[9](0, a[2] - 1, 3)}, {}] = , [{[2 a[2]], [{[2 a[2] + 1]}, {[2 a[2] + 1]}]}, {}] = , [2 a[2] + 1] For the domain, {a[1] = 1, a[3] = 2, 1 <= a[2]} The value of the game = , [{f[7](1, a[2], 1, 0) + [1], f[9](1, a[2] - 1, 3)}, {}] = , [{[2 a[2] + 1], [{[2 a[2] + 2]}, {[2 a[2] + 2]}]}, {}] = , [2 a[2] + 2] For the domain, {a[1] = 2, a[3] = 2, 1 <= a[2]} The value of the game = , [{f[9](2, a[2] - 1, 3), f[7](2, a[2], 1, 0) + [1]}, {}] = , [{[2 a[2] + 2], [{[2 a[2] + 3]}, {[2 a[2] + 3]}]}, {}] = , [2 a[2] + 3] For the domain, {a[3] = 2, 1 <= a[2], a[1] = 3} The value of the game = , [{f[7](3, a[2], 1, 0) + [1], f[9](3, a[2] - 1, 3)}, {}] = , [{[{[2 a[2] + 7/2]}, {[2 a[2] + 7/2]}], [2 a[2] + 3]}, {}] = , [2 a[2] + 4] For the domain, {a[3] = 2, 1 <= a[2], 4 <= a[1]} The value of the game = , [{f[7](a[1], a[2], 1, 0) + [1], f[9](a[1], a[2] - 1, 3)}, {}] = , [{[a[1] + 2 a[2]]}, {}] = , [a[1] + 2 a[2] + 1] For the domain, {3 <= a[3], 0 <= a[1], 1 <= a[2]} The value of the game = , [{f[7](a[1], a[2], a[3] - 1, 0) + [1], f[9](a[1], a[2] - 1, a[3] + 1)}, {}] = , [{[a[1] + 2 a[2] - 2 + a[3]], [{[a[1] + 2 a[2] + a[3] - 1]}, {[a[1] + 2 a[2] + a[3] - 1]}]} , {}] = , [a[1] + 2 a[2] + a[3] - 1] ########## #, f[10], # ########## For the domain, {a[1] = 0, a[2] = 1} The value of the game = , [{f[9](0, 0, 0) + [2]}, {}] = , [{[1]}, {}] = , [2] For the domain, {a[1] = 1, a[2] = 1} The value of the game = , [{f[9](1, 0, 0) + [2]}, {}] = , [{[3/2]}, {}] = , [2] For the domain, {2 <= a[1], a[2] = 1} The value of the game = , [{f[9](a[1], 0, 0) + [2]}, {}] = , [{[{[{[1 + a[1]]}, {[1 + a[1]]}]}, {[2]}]}, {}] = , [2] For the domain, {0 <= a[1], a[2] = 2} The value of the game = , [{f[9](a[1], 1, 0) + [2]}, {}] = , [{[{[{[{[a[1] + 2]}, {[a[1] + 2]}]}, {[5]}]}, {[4]}]}, {}] = , [4] For the domain, {3 <= a[2], 0 <= a[1]} The value of the game = , [{f[9](a[1], a[2] - 1, 0) + [2]}, {}] = , [{[{[{[a[1] + 2 a[2] - 3]}, {[2 a[2] + 1]}]}, {[2 a[2]]}]}, {} ] = , [2 a[2]] For the domain, {a[2] = 0, 0 <= a[1]} The value of the game = , [{}, {}] = , [{}, {}] = , [0] ###The conjectures is proved### >