> #restart; read `d:/Ake/tf/ToadsAndFrogs.txt`; > Prove(5,1,a); ##Conjectures## ############################# Let, f[1], be the value of , [T $ a[1], B, T $ a[2], B, T $ a[3], B, T $ a[4], B, T $ a[5], B, T $ a[6], F] ############################# f[1](0, 0, 0, 0, 0, 0) = [-5] f[1](a[1], 0, 0, 0, 0, 0) = [{[4 a[1] - 4]}, {[4 a[1] - 4]}], 1 <= a[1] f[1](a[1], a[2], 0, 0, 0, 0) = [4 a[1] + 3 a[2] - 3], 1 <= a[2], 0 <= a[1] f[1](a[1], a[2], 1, 0, 0, 0) = [4 a[1] + 3 a[2] - 1], 0 <= a[1], 0 <= a[2] f[1](a[1], a[2], a[3], 0, 0, 0) = [ {[4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}], 2 <= a[3], 0 <= a[1], 0 <= a[2] f[1](a[1], 0, 0, 1, 0, 0) = [4 a[1] - 2], 0 <= a[1] f[1](a[1], a[2], 0, 1, 0, 0) = [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}], 1 <= a[2], 0 <= a[1] f[1](a[1], a[2], a[3], 1, 0, 0) = [4 a[1] + 3 a[2] + 2 a[3]], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[1](a[1], a[2], a[3], a[4], 0, 0) = [4 a[1] + 3 a[2] + 2 a[3]], 2 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3] f[1](0, 0, 0, 0, 1, 0) = [-3] f[1](a[1], 0, 0, 0, 1, 0) = [{[4 a[1] - 2]}, {[4 a[1] - 2]}], 1 <= a[1] f[1](a[1], a[2], 0, 0, 1, 0) = [4 a[1] + 3 a[2] - 1], 1 <= a[2], 0 <= a[1] f[1](a[1], a[2], a[3], 0, 1, 0) = [4 a[1] + 3 a[2] - 1], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[1](a[1], a[2], 0, 1, 1, 0) = [4 a[1] + 3 a[2]], 0 <= a[1], 0 <= a[2] f[1](a[1], a[2], a[3], 1, 1, 0) = [ {[4 a[1] + 3 a[2] + 2 a[3] + 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[1](a[1], a[2], a[3], a[4], 1, 0) = [ {[4 a[1] + 3 a[2] + 2 a[3] + 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}], 2 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3] f[1](a[1], 0, 0, 0, 2, 0) = [4 a[1] - 1], 0 <= a[1] f[1](a[1], a[2], 0, 0, 2, 0) = [{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}], 1 <= a[2], 0 <= a[1] f[1](a[1], a[2], a[3], 0, 2, 0) = [{[{[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[1](a[1], a[2], a[3], a[4], 2, 0) = [{[ {[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}], 0 <= a[1], 0 <= a[2], 0 <= a[3], 1 <= a[4] f[1](a[1], a[2], a[3], a[4], a[5], 0) = [{[ {[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}], 0 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3], 3 <= a[5] f[1](0, 0, 0, 0, 0, 1) = [-4] f[1](a[1], 0, 0, 0, 0, 1) = [{[4 a[1] - 3]}, {[4 a[1] - 3]}], 1 <= a[1] f[1](a[1], a[2], 0, 0, 0, 1) = [4 a[1] + 3 a[2] - 2], 1 <= a[2], 0 <= a[1] f[1](a[1], a[2], 1, 0, 0, 1) = [4 a[1] + 3 a[2]], 0 <= a[1], 0 <= a[2] f[1](a[1], a[2], a[3], 0, 0, 1) = [ {[4 a[1] + 3 a[2] + 2 a[3] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] - 1]}], 2 <= a[3], 0 <= a[1], 0 <= a[2] f[1](a[1], 0, 0, 1, 0, 1) = [4 a[1] - 1], 0 <= a[1] f[1](a[1], a[2], 0, 1, 0, 1) = [{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}], 1 <= a[2], 0 <= a[1] f[1](a[1], a[2], a[3], 1, 0, 1) = [4 a[1] + 3 a[2] + 2 a[3] + 1], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[1](a[1], a[2], a[3], a[4], 0, 1) = [4 a[1] + 3 a[2] + 2 a[3] + 1] , 2 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3] f[1](a[1], 0, 0, 0, 1, 1) = [{[5 a[1]]}, {[4 a[1] - 1]}], 0 <= a[1] f[1](a[1], a[2], 0, 0, 1, 1) = [{[5 a[1] + 4 a[2]]}, {[{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}]}], 1 <= a[2], 0 <= a[1] f[1](a[1], a[2], a[3], 0, 1, 1) = [{[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[1](a[1], a[2], a[3], a[4], 1, 1) = [{[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}], 0 <= a[1], 0 <= a[2], 0 <= a[3], 1 <= a[4] f[1](a[1], a[2], a[3], a[4], a[5], 1) = [ {[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}], 2 <= a[5], 0 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3] f[1](a[1], a[2], a[3], a[4], a[5], a[6]) = [5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5]], 0 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3], 0 <= a[5], 2 <= a[6] ############################# Let, f[2], be the value of , [T $ a[1], B, T $ a[2], B, T $ a[3], B, T $ a[4], B, T $ a[5], F, B] ############################# f[2](a[1], 0, 0, 0, 0) = [4 a[1] - 4], 0 <= a[1] f[2](a[1], a[2], 0, 0, 0) = [{[4 a[1] + 3 a[2] - 3]}, {[4 a[1] + 3 a[2] - 3]}], 1 <= a[2], 0 <= a[1] f[2](a[1], a[2], a[3], 0, 0) = [4 a[1] + 3 a[2] + 2 a[3] - 2], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[2](a[1], a[2], 0, 1, 0) = [4 a[1] + 3 a[2] - 1], 0 <= a[1], 0 <= a[2] f[2](a[1], a[2], a[3], a[4], 0) = [ {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}], 2 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3] f[2](a[1], a[2], a[3], 1, 0) = [{[4 a[1] + 3 a[2] + 2 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[2](a[1], 0, 0, 0, 1) = [4 a[1] - 2], 0 <= a[1] f[2](a[1], a[2], 0, 0, 1) = [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}], 1 <= a[2], 0 <= a[1] f[2](a[1], a[2], a[3], 0, 1) = [4 a[1] + 3 a[2] + 2 a[3]], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[2](a[1], a[2], a[3], a[4], 1) = [4 a[1] + 3 a[2] + 2 a[3]], 0 <= a[1], 0 <= a[2], 0 <= a[3], 1 <= a[4] f[2](a[1], a[2], a[3], a[4], a[5]) = [4 a[1] + 3 a[2] + 2 a[3] + a[4]], 2 <= a[5], 0 <= a[4], 0 <= a[1], 0 <= a[2], 0 <= a[3] ############################# Let, f[3], be the value of , [T $ a[1], B, T $ a[2], B, T $ a[3], B, T $ a[4], F, B, B] ############################# f[3](a[1], a[2], 0, 0) = [4 a[1] + 3 a[2] - 3], 0 <= a[1], 0 <= a[2] f[3](a[1], a[2], a[3], 0) = [{[4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}], 0 <= a[1], 0 <= a[2], 1 <= a[3] f[3](a[1], a[2], a[3], a[4]) = [4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1], 0 <= a[1], 0 <= a[2], 0 <= a[3], 1 <= a[4] ############################# Let, f[4], be the value of , [T $ a[1], B, T $ a[2], B, T $ a[3], F, B, B, B] ############################# f[4](a[1], a[2], a[3]) = [4 a[1] + 3 a[2] + 2 a[3] - 2], 0 <= a[1], 0 <= a[2], 0 <= a[3] ############################# Let, f[5], be the value of , [T $ a[1], B, T $ a[2], F, B, B, B, B] ############################# f[5](a[1], a[2]) = [4 a[1] + 3 a[2] - 1], 0 <= a[1], 0 <= a[2] ############################# Let, f[6], be the value of , [T $ a[1], F, B, B, B, B, B] ############################# f[6](a[1]) = [4 a[1]], 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[3] = 0, a[2] = 0, a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{}, {f[2](0, 0, 0, 0, 0) + [0]}] = , [{}, {[-4]}] = , [-5] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](a[1] - 1, 1, 0, 0, 0, 0)}, {f[2](a[1], 0, 0, 0, 0) + [0]}] = , [{[4 a[1] - 4]}, {[4 a[1] - 4]}] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 0, 0, 0), f[1](a[1], a[2] - 1, 1, 0, 0, 0)}, {f[2](a[1], a[2], 0, 0, 0) + [0]}] = , [{[4 a[1] - 4 + 3 a[2]]}, {[{[4 a[1] + 3 a[2] - 3]}, {[4 a[1] + 3 a[2] - 3]}]}] = , [4 a[1] + 3 a[2] - 3] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](0, a[2] - 1, 1, 0, 0, 0)}, {f[2](0, a[2], 0, 0, 0) + [0]}] = , [{[-4 + 3 a[2]]}, {[{[-3 + 3 a[2]]}, {[-3 + 3 a[2]]}]}] = , [-3 + 3 a[2]] For the domain, { 1 <= a[2], a[3] = 1, 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 1, 0, 0, 0), f[1](a[1], a[2] - 1, 2, 0, 0, 0), f[1](a[1], a[2], 0, 1, 0, 0)}, {f[2](a[1], a[2], 1, 0, 0) + [0]}] = , [{[4 a[1] + 3 a[2] - 2], [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}]}, {[4 a[1] + 3 a[2]]}] = , [4 a[1] + 3 a[2] - 1] For the domain, {a[2] = 0, a[3] = 1, 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [ {f[1](a[1] - 1, 1, 1, 0, 0, 0), f[1](a[1], 0, 0, 1, 0, 0)}, {f[2](a[1], 0, 1, 0, 0) + [0]}] = , [{[4 a[1] - 2]}, {[4 a[1]]}] = , [4 a[1] - 1] For the domain, {a[1] = 0, 1 <= a[2], a[3] = 1, a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [ {f[1](0, a[2], 0, 1, 0, 0), f[1](0, a[2] - 1, 2, 0, 0, 0)}, {f[2](0, a[2], 1, 0, 0) + [0]}] = , [{[{[-1 + 3 a[2]]}, {[-1 + 3 a[2]]}]}, {[3 a[2]]}] = , [-1 + 3 a[2]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 1, a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](0, 0, 0, 1, 0, 0)}, {f[2](0, 0, 1, 0, 0) + [0]}] = , [{[-2]}, {[0]}] = , [-1] For the domain, { 1 <= a[2], 2 <= a[3], 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 0 } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], 0, 0, 0), f[1](a[1], a[2] - 1, a[3] + 1, 0, 0, 0), f[1](a[1], a[2], a[3] - 1, 1, 0, 0)}, {f[2](a[1], a[2], a[3], 0, 0) + [0]}] = , [{[{[4 a[1] - 3 + 3 a[2] + 2 a[3]]}, {[4 a[1] - 3 + 3 a[2] + 2 a[3]]}], [4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}] For the domain, { a[2] = 0, 2 <= a[3], 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 1, 0, 0), f[1](a[1] - 1, 1, a[3], 0, 0, 0)}, {f[2](a[1], 0, a[3], 0, 0) + [0]}] = , [{[{[4 a[1] - 3 + 2 a[3]]}, {[4 a[1] - 3 + 2 a[3]]}], [4 a[1] - 2 + 2 a[3]]}, {[4 a[1] - 2 + 2 a[3]]}] = , [{[4 a[1] - 2 + 2 a[3]]}, {[4 a[1] - 2 + 2 a[3]]}] For the domain, { a[1] = 0, 1 <= a[2], 2 <= a[3], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](0, a[2], a[3] - 1, 1, 0, 0), f[1](0, a[2] - 1, a[3] + 1, 0, 0, 0)}, {f[2](0, a[2], a[3], 0, 0) + [0]}] = , [{[-2 + 3 a[2] + 2 a[3]], [{[-3 + 3 a[2] + 2 a[3]]}, {[-3 + 3 a[2] + 2 a[3]]}]}, {[-2 + 3 a[2] + 2 a[3]]}] = , [{[-2 + 3 a[2] + 2 a[3]]}, {[-2 + 3 a[2] + 2 a[3]]}] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[3], a[4] = 0, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](0, 0, a[3] - 1, 1, 0, 0)}, {f[2](0, 0, a[3], 0, 0) + [0]}] = , [{[-2 + 2 a[3]]}, {[-2 + 2 a[3]]}] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 1, a[5] = 0, a[6] = 0} The value of the game = , [ {f[1](a[1] - 1, 1, 0, 1, 0, 0), f[1](a[1], 0, 0, 0, 1, 0)}, {f[2](a[1], 0, 0, 1, 0) + [0]}] = , [{[{[4 a[1] - 2]}, {[4 a[1] - 2]}]}, {[4 a[1] - 1]}] = , [4 a[1] - 2] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 1, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](0, 0, 0, 0, 1, 0)}, {f[2](0, 0, 0, 1, 0) + [0]}] = , [{[-3]}, {[-1]}] = , [-2] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 1, a[5] = 0, a[6] = 0} The value of the game = , [{f[1](a[1], a[2] - 1, 1, 1, 0, 0), f[1](a[1] - 1, a[2] + 1, 0, 1, 0, 0), f[1](a[1], a[2], 0, 0, 1, 0)}, {f[2](a[1], a[2], 0, 1, 0) + [0]}] = , [{[{[4 a[1] + 3 a[2] - 2]}, {[4 a[1] + 3 a[2] - 2]}], [4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}] = , [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 1, a[5] = 0, a[6] = 0} The value of the game = , [ {f[1](0, a[2], 0, 0, 1, 0), f[1](0, a[2] - 1, 1, 1, 0, 0)}, {f[2](0, a[2], 0, 1, 0) + [0]}] = , [{[-1 + 3 a[2]]}, {[-1 + 3 a[2]]}] For the domain, { 1 <= a[2], 1 <= a[1], a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 0 } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], 1, 0, 0), f[1](a[1], a[2], a[3] - 1, 2, 0, 0), f[1](a[1], a[2] - 1, a[3] + 1, 1, 0, 0), f[1](a[1], a[2], a[3], 0, 1, 0)}, {f[2](a[1], a[2], a[3], 1, 0) + [0]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 1]}, { [{[4 a[1] + 3 a[2] + 2 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}]} ] = , [4 a[1] + 3 a[2] + 2 a[3]] For the domain, { a[2] = 0, 1 <= a[1], a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](a[1], 0, a[3], 0, 1, 0), f[1](a[1], 0, a[3] - 1, 2, 0, 0), f[1](a[1] - 1, 1, a[3], 1, 0, 0)}, {f[2](a[1], 0, a[3], 1, 0) + [0]}] = , [{[4 a[1] - 1 + 2 a[3]]}, {[{[4 a[1] + 2 a[3]]}, {[4 a[1] + 2 a[3]]}]}] = , [4 a[1] + 2 a[3]] For the domain, { a[1] = 0, 1 <= a[2], a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](0, a[2], a[3], 0, 1, 0), f[1](0, a[2] - 1, a[3] + 1, 1, 0, 0), f[1](0, a[2], a[3] - 1, 2, 0, 0)}, {f[2](0, a[2], a[3], 1, 0) + [0]}] = , [{[-1 + 3 a[2] + 2 a[3]]}, {[{[3 a[2] + 2 a[3]]}, {[3 a[2] + 2 a[3]]}]}] = , [3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 0} The value of the game = , [ {f[1](0, 0, a[3] - 1, 2, 0, 0), f[1](0, 0, a[3], 0, 1, 0)}, {f[2](0, 0, a[3], 1, 0) + [0]}] = , [{[-1 + 2 a[3]]}, {[{[2 a[3]]}, {[2 a[3]]}]}] = , [2 a[3]] For the domain, {1 <= a[2], 1 <= a[1], a[5] = 0, 3 <= a[4], 1 <= a[3], a[6] = 0} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], 0, 0), f[1](a[1], a[2] - 1, a[3] + 1, a[4], 0, 0), f[1](a[1], a[2], a[3], a[4] - 1, 1, 0), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 0, 0)}, {f[2](a[1], a[2], a[3], a[4], 0) + [0]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 2], [%1, %1]}, {[%1, %1]} ] %1 := {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]} = , [4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1] For the domain, { 1 <= a[2], 1 <= a[1], a[5] = 0, a[4] = 2, 1 <= a[3], a[6] = 0 } The value of the game = , [{f[1](a[1], a[2], a[3] - 1, 3, 0, 0), f[1](a[1], a[2], a[3], 1, 1, 0), f[1](a[1], a[2] - 1, a[3] + 1, 2, 0, 0), f[1](a[1] - 1, a[2] + 1, a[3], 2, 0, 0)}, {f[2](a[1], a[2], a[3], 2, 0) + [0]}] = , [{[4 a[1] + 3 a[2] + 2 a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[4 a[1] + 3 a[2] + 2 a[3] + 1]} = , [4 a[1] + 3 a[2] + 2 a[3] + 1] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 0, a[4] = 2, a[6] = 0} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 2, 0, 0), f[1](a[1], a[2] - 1, 1, 2, 0, 0), f[1](a[1], a[2], 0, 1, 1, 0)}, {f[2](a[1], a[2], 0, 2, 0) + [0]}] = , [{[4 a[1] + 3 a[2]]}, {[{[4 a[1] + 3 a[2] + 1]}, {[4 a[1] + 3 a[2] + 1]}]}] = , [4 a[1] + 3 a[2] + 1] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 0, 3 <= a[4], a[6] = 0 } The value of the game = , [{f[1](a[1], a[2], 0, a[4] - 1, 1, 0), f[1](a[1], a[2] - 1, 1, a[4], 0, 0), f[1](a[1] - 1, a[2] + 1, 0, a[4], 0, 0)}, {f[2](a[1], a[2], 0, a[4], 0) + [0]}] = , [{[%1, %1], [4 a[1] + 3 a[2] - 2 + a[4]]}, {[%1, %1]}] %1 := {[4 a[1] + 3 a[2] - 1 + a[4]]} = , [4 a[1] + 3 a[2] - 1 + a[4]] For the domain, { a[2] = 0, 1 <= a[1], a[5] = 0, 3 <= a[4], 1 <= a[3], a[6] = 0 } The value of the game = , [{ f[1](a[1], 0, a[3] - 1, a[4] + 1, 0, 0), f[1](a[1], 0, a[3], a[4] - 1, 1, 0), f[1](a[1] - 1, 1, a[3], a[4], 0, 0)}, {f[2](a[1], 0, a[3], a[4], 0) + [0]}] = , [{[%1, %1], [4 a[1] - 2 + 2 a[3] + a[4]]}, {[%1, %1]}] %1 := {[4 a[1] - 1 + 2 a[3] + a[4]]} = , [4 a[1] - 1 + 2 a[3] + a[4]] For the domain, { a[2] = 0, 1 <= a[1], a[5] = 0, a[4] = 2, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](a[1] - 1, 1, a[3], 2, 0, 0), f[1](a[1], 0, a[3], 1, 1, 0), f[1](a[1], 0, a[3] - 1, 3, 0, 0)}, {f[2](a[1], 0, a[3], 2, 0) + [0]}] = , [{[%1, %1], [4 a[1] + 2 a[3]]}, {[%1, %1]}] %1 := {[4 a[1] + 1 + 2 a[3]]} = , [4 a[1] + 1 + 2 a[3]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 0, a[4] = 2, a[6] = 0} The value of the game = , [ {f[1](a[1] - 1, 1, 0, 2, 0, 0), f[1](a[1], 0, 0, 1, 1, 0)}, {f[2](a[1], 0, 0, 2, 0) + [0]}] = , [{[4 a[1]]}, {[{[4 a[1] + 1]}, {[4 a[1] + 1]}]}] = , [4 a[1] + 1] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 0, 3 <= a[4], a[6] = 0} The value of the game = , [{f[1](a[1], 0, 0, a[4] - 1, 1, 0), f[1](a[1] - 1, 1, 0, a[4], 0, 0)}, {f[2](a[1], 0, 0, a[4], 0) + [0]}] = , [{[%1, %1], [4 a[1] - 2 + a[4]]}, {[%1, %1]}] %1 := {[4 a[1] - 1 + a[4]]} = , [4 a[1] - 1 + a[4]] For the domain, { a[1] = 0, 1 <= a[2], a[5] = 0, 3 <= a[4], 1 <= a[3], a[6] = 0 } The value of the game = , [{ f[1](0, a[2], a[3] - 1, a[4] + 1, 0, 0), f[1](0, a[2], a[3], a[4] - 1, 1, 0), f[1](0, a[2] - 1, a[3] + 1, a[4], 0, 0)}, {f[2](0, a[2], a[3], a[4], 0) + [0]}] = , [{[-2 + 3 a[2] + 2 a[3] + a[4]], [%1, %1]}, {[%1, %1]}] %1 := {[-1 + 3 a[2] + 2 a[3] + a[4]]} = , [-1 + 3 a[2] + 2 a[3] + a[4]] For the domain, { a[1] = 0, 1 <= a[2], a[5] = 0, a[4] = 2, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](0, a[2] - 1, a[3] + 1, 2, 0, 0), f[1](0, a[2], a[3], 1, 1, 0), f[1](0, a[2], a[3] - 1, 3, 0, 0)}, {f[2](0, a[2], a[3], 2, 0) + [0]}] = , [{[3 a[2] + 2 a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[1 + 3 a[2] + 2 a[3]]} = , [1 + 3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 0, a[4] = 2, a[6] = 0} The value of the game = , [ {f[1](0, a[2], 0, 1, 1, 0), f[1](0, a[2] - 1, 1, 2, 0, 0)}, {f[2](0, a[2], 0, 2, 0) + [0]}] = , [{[3 a[2]]}, {[{[1 + 3 a[2]]}, {[1 + 3 a[2]]}]}] = , [1 + 3 a[2]] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 0, 3 <= a[4], a[6] = 0} The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], 0, 0), f[1](0, a[2], 0, a[4] - 1, 1, 0)}, {f[2](0, a[2], 0, a[4], 0) + [0]}] = , [{[-2 + 3 a[2] + a[4]], [%1, %1]}, {[%1, %1]}] %1 := {[-1 + 3 a[2] + a[4]]} = , [-1 + 3 a[2] + a[4]] For the domain, { a[1] = 0, a[2] = 0, a[5] = 0, 3 <= a[4], 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](0, 0, a[3], a[4] - 1, 1, 0), f[1](0, 0, a[3] - 1, a[4] + 1, 0, 0)}, {f[2](0, 0, a[3], a[4], 0) + [0]}] = , [{[-2 + 2 a[3] + a[4]], [%1, %1]}, {[%1, %1]}] %1 := {[-1 + 2 a[3] + a[4]]} = , [-1 + 2 a[3] + a[4]] For the domain, {a[1] = 0, a[2] = 0, a[5] = 0, a[4] = 2, 1 <= a[3], a[6] = 0} The value of the game = , [ {f[1](0, 0, a[3] - 1, 3, 0, 0), f[1](0, 0, a[3], 1, 1, 0)}, {f[2](0, 0, a[3], 2, 0) + [0]}] = , [{[2 a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[1 + 2 a[3]]} = , [1 + 2 a[3]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 0, a[4] = 2, a[6] = 0} The value of the game = , [{f[1](0, 0, 0, 1, 1, 0)}, {f[2](0, 0, 0, 2, 0) + [0]}] = , [{[0]}, {[{[1]}, {[1]}]}] = , [1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 0, 3 <= a[4], a[6] = 0} The value of the game = , [{f[1](0, 0, 0, a[4] - 1, 1, 0)}, {f[2](0, 0, 0, a[4], 0) + [0]}] = , [{[{[a[4] - 1]}, {[a[4] - 1]}]}, {[{[a[4] - 1]}, {[a[4] - 1]}]}] = , [a[4] - 1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [{f[1](0, 0, 0, 0, 0, 1)}, {f[2](0, 0, 0, 0, 1) + [0]}] = , [{[-4]}, {[-2]}] = , [-3] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [ {f[1](a[1], 0, 0, 0, 0, 1), f[1](a[1] - 1, 1, 0, 0, 1, 0)}, {f[2](a[1], 0, 0, 0, 1) + [0]}] = , [{[{[4 a[1] - 3]}, {[4 a[1] - 3]}], [4 a[1] - 2]}, {[4 a[1] - 2]}] = , [{[4 a[1] - 2]}, {[4 a[1] - 2]}] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 0, 1, 0), f[1](a[1], a[2] - 1, 1, 0, 1, 0), f[1](a[1], a[2], 0, 0, 0, 1)}, {f[2](a[1], a[2], 0, 0, 1) + [0]}] = , [{[4 a[1] + 3 a[2] - 2]}, {[{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}]}] = , [4 a[1] + 3 a[2] - 1] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [ {f[1](0, a[2], 0, 0, 0, 1), f[1](0, a[2] - 1, 1, 0, 1, 0)}, {f[2](0, a[2], 0, 0, 1) + [0]}] = , [{[-2 + 3 a[2]]}, {[{[-1 + 3 a[2]]}, {[-1 + 3 a[2]]}]}] = , [-1 + 3 a[2]] For the domain, { 1 <= a[2], a[3] = 1, 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [{f[1](a[1], a[2], 0, 1, 1, 0), f[1](a[1], a[2], 1, 0, 0, 1), f[1](a[1] - 1, a[2] + 1, 1, 0, 1, 0), f[1](a[1], a[2] - 1, 2, 0, 1, 0)}, {f[2](a[1], a[2], 1, 0, 1) + [0]}] = , [{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2] + 2]}] = , [4 a[1] + 3 a[2] + 1] For the domain, { 1 <= a[2], 2 <= a[3], 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 0 } The value of the game = , [{ f[1](a[1], a[2] - 1, a[3] + 1, 0, 1, 0), f[1](a[1] - 1, a[2] + 1, a[3], 0, 1, 0), f[1](a[1], a[2], a[3], 0, 0, 1), f[1](a[1], a[2], a[3] - 1, 1, 1, 0)}, {f[2](a[1], a[2], a[3], 0, 1) + [0]}] = , [{[{[4 a[1] + 3 a[2] + 2 a[3] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] - 1]}], [4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3]]} ] = , [4 a[1] + 3 a[2] + 2 a[3] - 1] For the domain, {a[2] = 0, a[3] = 1, 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [{f[1](a[1], 0, 0, 1, 1, 0), f[1](a[1] - 1, 1, 1, 0, 1, 0), f[1](a[1], 0, 1, 0, 0, 1)}, {f[2](a[1], 0, 1, 0, 1) + [0]}] = , [{[4 a[1]]}, {[4 a[1] + 2]}] = , [4 a[1] + 1] For the domain, { a[2] = 0, 2 <= a[3], 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 1, 1, 0), f[1](a[1], 0, a[3], 0, 0, 1), f[1](a[1] - 1, 1, a[3], 0, 1, 0)}, {f[2](a[1], 0, a[3], 0, 1) + [0]}] = , [{[4 a[1] - 2 + 2 a[3]], [{[4 a[1] - 1 + 2 a[3]]}, {[4 a[1] - 1 + 2 a[3]]}]}, {[4 a[1] + 2 a[3]]}] = , [4 a[1] - 1 + 2 a[3]] For the domain, {a[1] = 0, 1 <= a[2], a[3] = 1, a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [{f[1](0, a[2], 0, 1, 1, 0), f[1](0, a[2] - 1, 2, 0, 1, 0), f[1](0, a[2], 1, 0, 0, 1)}, {f[2](0, a[2], 1, 0, 1) + [0]}] = , [{[3 a[2]]}, {[3 a[2] + 2]}] = , [1 + 3 a[2]] For the domain, { a[1] = 0, 1 <= a[2], 2 <= a[3], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [{f[1](0, a[2], a[3] - 1, 1, 1, 0), f[1](0, a[2], a[3], 0, 0, 1), f[1](0, a[2] - 1, a[3] + 1, 0, 1, 0)}, {f[2](0, a[2], a[3], 0, 1) + [0]}] = , [{[-2 + 3 a[2] + 2 a[3]], [{[-1 + 3 a[2] + 2 a[3]]}, {[-1 + 3 a[2] + 2 a[3]]}]}, {[3 a[2] + 2 a[3]]}] = , [-1 + 3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 1, a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [ {f[1](0, 0, 0, 1, 1, 0), f[1](0, 0, 1, 0, 0, 1)}, {f[2](0, 0, 1, 0, 1) + [0]}] = , [{[0]}, {[2]}] = , [1] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[3], a[5] = 1, a[4] = 0, a[6] = 0} The value of the game = , [ {f[1](0, 0, a[3], 0, 0, 1), f[1](0, 0, a[3] - 1, 1, 1, 0)}, {f[2](0, 0, a[3], 0, 1) + [0]}] = , [{[{[-1 + 2 a[3]]}, {[-1 + 2 a[3]]}]}, {[2 a[3]]}] = , [-1 + 2 a[3]] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 1, a[6] = 0} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 1, 1, 0), f[1](a[1], a[2], 0, 1, 0, 1), f[1](a[1], a[2] - 1, 1, 1, 1, 0), f[1](a[1], a[2], 0, 0, 2, 0)}, {f[2](a[1], a[2], 0, 1, 1) + [0]}] = , [{[{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}], [4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] + 1]}] = , [4 a[1] + 3 a[2]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 1, a[6] = 0} The value of the game = , [{f[1](a[1], 0, 0, 0, 2, 0), f[1](a[1], 0, 0, 1, 0, 1), f[1](a[1] - 1, 1, 0, 1, 1, 0)}, {f[2](a[1], 0, 0, 1, 1) + [0]}] = , [{[4 a[1] - 1]}, {[4 a[1] + 1]}] = , [4 a[1]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 1, a[4] = 1, a[6] = 0} The value of the game = , [{f[1](0, a[2], 0, 0, 2, 0), f[1](0, a[2] - 1, 1, 1, 1, 0), f[1](0, a[2], 0, 1, 0, 1)}, {f[2](0, a[2], 0, 1, 1) + [0]}] = , [{[{[3 a[2]]}, {[3 a[2]]}]}, {[3 a[2] + 1]}] = , [3 a[2]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 1, a[4] = 1, a[6] = 0} The value of the game = , [ {f[1](0, 0, 0, 1, 0, 1), f[1](0, 0, 0, 0, 2, 0)}, {f[2](0, 0, 0, 1, 1) + [0]}] = , [{[-1]}, {[1]}] = , [0] For the domain, { 1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 1, 1 <= a[3], a[6] = 0 } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], 1, 1, 0), f[1](a[1], a[2] - 1, a[3] + 1, 1, 1, 0), f[1](a[1], a[2], a[3] - 1, 2, 1, 0), f[1](a[1], a[2], a[3], 0, 2, 0), f[1](a[1], a[2], a[3], 1, 0, 1)}, {f[2](a[1], a[2], a[3], 1, 1) + [0]}] = , [{%1, [{[{[5 a[1] + 4 a[2] + 3 a[3]]}, {%1}]}, %2], [%2, %2]}, {%1}] %1 := [4 a[1] + 3 a[2] + 2 a[3] + 1] %2 := {[4 a[1] + 3 a[2] + 2 a[3]]} = , [{[4 a[1] + 3 a[2] + 2 a[3] + 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}] For the domain, { a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 1, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](a[1], 0, a[3], 1, 0, 1), f[1](a[1], 0, a[3], 0, 2, 0), f[1](a[1], 0, a[3] - 1, 2, 1, 0), f[1](a[1] - 1, 1, a[3], 1, 1, 0)}, {f[2](a[1], 0, a[3], 1, 1) + [0]}] = , [{[{[{[5 a[1] + 3 a[3]]}, {[4 a[1] + 2 a[3] + 1]}]}, {[4 a[1] + 2 a[3]]}], [4 a[1] + 2 a[3] + 1], [{[4 a[1] + 2 a[3]]}, {[4 a[1] + 2 a[3]]}]}, {[4 a[1] + 2 a[3] + 1]}] = , [{[4 a[1] + 2 a[3] + 1]}, {[4 a[1] + 2 a[3] + 1]}] For the domain, { a[1] = 0, 1 <= a[2], a[5] = 1, a[4] = 1, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](0, a[2], a[3], 1, 0, 1), f[1](0, a[2], a[3], 0, 2, 0), f[1](0, a[2], a[3] - 1, 2, 1, 0), f[1](0, a[2] - 1, a[3] + 1, 1, 1, 0)}, {f[2](0, a[2], a[3], 1, 1) + [0]}] = , [{[{[{[4 a[2] + 3 a[3]]}, {[3 a[2] + 2 a[3] + 1]}]}, {[3 a[2] + 2 a[3]]}], [{[3 a[2] + 2 a[3]]}, {[3 a[2] + 2 a[3]]}], [3 a[2] + 2 a[3] + 1]}, {[3 a[2] + 2 a[3] + 1]}] = , [{[3 a[2] + 2 a[3] + 1]}, {[3 a[2] + 2 a[3] + 1]}] For the domain, {a[1] = 0, a[2] = 0, a[5] = 1, a[4] = 1, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](0, 0, a[3] - 1, 2, 1, 0), f[1](0, 0, a[3], 0, 2, 0), f[1](0, 0, a[3], 1, 0, 1)}, {f[2](0, 0, a[3], 1, 1) + [0]}] = , [{[2 a[3] + 1], [{[2 a[3]]}, {[2 a[3]]}], [{[{[3 a[3]]}, {[2 a[3] + 1]}]}, {[2 a[3]]}]}, {[2 a[3] + 1]} ] = , [{[2 a[3] + 1]}, {[2 a[3] + 1]}] For the domain, {1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 1, 1 <= a[3], a[6] = 0} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], 1, 0), f[1](a[1], a[2], a[3], a[4] - 1, 2, 0), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 1, 0), f[1](a[1], a[2] - 1, a[3] + 1, a[4], 1, 0), f[1](a[1], a[2], a[3], a[4], 0, 1)}, {f[2](a[1], a[2], a[3], a[4], 1) + [0]}] = , [{%1, [{[{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] - 2]}, {%1}]}, %2], [%2, %2]}, {%1}] %1 := [4 a[1] + 3 a[2] + 2 a[3] + a[4]] %2 := {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]} = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}] For the domain, { a[3] = 0, 1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 1, a[6] = 0 } The value of the game = , [{f[1](a[1], a[2], 0, a[4], 0, 1), f[1](a[1], a[2] - 1, 1, a[4], 1, 0), f[1](a[1], a[2], 0, a[4] - 1, 2, 0), f[1](a[1] - 1, a[2] + 1, 0, a[4], 1, 0)}, {f[2](a[1], a[2], 0, a[4], 1) + [0]}] = , [{[4 a[1] + 3 a[2] + a[4]], [{[ {[5 a[1] + 4 a[2] - 2 + 2 a[4]]}, {[4 a[1] + 3 a[2] + a[4]]}] }, %1], [%1, %1]}, {[4 a[1] + 3 a[2] + a[4]]}] %1 := {[4 a[1] + 3 a[2] - 1 + a[4]]} = , [{[4 a[1] + 3 a[2] + a[4]]}, {[4 a[1] + 3 a[2] + a[4]]}] For the domain, { a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 1, 1 <= a[3], a[6] = 0 } The value of the game = , [{f[1](a[1], 0, a[3], a[4], 0, 1), f[1](a[1], 0, a[3] - 1, a[4] + 1, 1, 0), f[1](a[1], 0, a[3], a[4] - 1, 2, 0), f[1](a[1] - 1, 1, a[3], a[4], 1, 0)}, {f[2](a[1], 0, a[3], a[4], 1) + [0]}] = , [{[4 a[1] + 2 a[3] + a[4]], [%1, %1], [{[ {[5 a[1] - 2 + 3 a[3] + 2 a[4]]}, {[4 a[1] + 2 a[3] + a[4]]}] }, %1]}, {[4 a[1] + 2 a[3] + a[4]]}] %1 := {[4 a[1] - 1 + 2 a[3] + a[4]]} = , [{[4 a[1] + 2 a[3] + a[4]]}, {[4 a[1] + 2 a[3] + a[4]]}] For the domain, { a[3] = 0, a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 1, a[6] = 0} The value of the game = , [{f[1](a[1], 0, 0, a[4], 0, 1), f[1](a[1] - 1, 1, 0, a[4], 1, 0), f[1](a[1], 0, 0, a[4] - 1, 2, 0)}, {f[2](a[1], 0, 0, a[4], 1) + [0]}] = , [{[{[{[5 a[1] - 2 + 2 a[4]]}, {[4 a[1] + a[4]]}]}, {[4 a[1] - 1 + a[4]]}], [{[4 a[1] - 1 + a[4]]}, {[4 a[1] - 1 + a[4]]}], [4 a[1] + a[4]]}, {[4 a[1] + a[4]]}] = , [{[4 a[1] + a[4]]}, {[4 a[1] + a[4]]}] For the domain, { a[1] = 0, 1 <= a[2], 2 <= a[4], a[5] = 1, 1 <= a[3], a[6] = 0 } The value of the game = , [{ f[1](0, a[2] - 1, a[3] + 1, a[4], 1, 0), f[1](0, a[2], a[3] - 1, a[4] + 1, 1, 0), f[1](0, a[2], a[3], a[4] - 1, 2, 0), f[1](0, a[2], a[3], a[4], 0, 1)}, {f[2](0, a[2], a[3], a[4], 1) + [0]}] = , [{[3 a[2] + 2 a[3] + a[4]], [{[ {[-2 + 4 a[2] + 3 a[3] + 2 a[4]]}, {[3 a[2] + 2 a[3] + a[4]]} ]}, %1], [%1, %1]}, {[3 a[2] + 2 a[3] + a[4]]}] %1 := {[-1 + 3 a[2] + 2 a[3] + a[4]]} = , [{[3 a[2] + 2 a[3] + a[4]]}, {[3 a[2] + 2 a[3] + a[4]]}] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[4], a[5] = 1, a[6] = 0} The value of the game = , [{f[1](0, a[2], 0, a[4], 0, 1), f[1](0, a[2], 0, a[4] - 1, 2, 0), f[1](0, a[2] - 1, 1, a[4], 1, 0)}, {f[2](0, a[2], 0, a[4], 1) + [0]}] = , [{[3 a[2] + a[4]], [ {[{[-2 + 4 a[2] + 2 a[4]]}, {[3 a[2] + a[4]]}]}, {[-1 + 3 a[2] + a[4]]}], [{[-1 + 3 a[2] + a[4]]}, {[-1 + 3 a[2] + a[4]]}]}, {[3 a[2] + a[4]]}] = , [{[3 a[2] + a[4]]}, {[3 a[2] + a[4]]}] For the domain, { a[1] = 0, a[2] = 0, 2 <= a[4], a[5] = 1, 1 <= a[3], a[6] = 0} The value of the game = , [{f[1](0, 0, a[3], a[4], 0, 1), f[1](0, 0, a[3], a[4] - 1, 2, 0), f[1](0, 0, a[3] - 1, a[4] + 1, 1, 0)}, {f[2](0, 0, a[3], a[4], 1) + [0]}] = , [{[{[{[-2 + 3 a[3] + 2 a[4]]}, {[2 a[3] + a[4]]}]}, {[-1 + 2 a[3] + a[4]]}], [{[-1 + 2 a[3] + a[4]]}, {[-1 + 2 a[3] + a[4]]}], [2 a[3] + a[4]]}, {[2 a[3] + a[4]]}] = , [{[2 a[3] + a[4]]}, {[2 a[3] + a[4]]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 2 <= a[4], a[5] = 1, a[6] = 0} The value of the game = , [ {f[1](0, 0, 0, a[4] - 1, 2, 0), f[1](0, 0, 0, a[4], 0, 1)}, {f[2](0, 0, 0, a[4], 1) + [0]}] = , [{[{[{[-2 + 2 a[4]]}, {[a[4]]}]}, {[a[4] - 1]}], [a[4]]}, {[a[4]]}] = , [{[a[4]]}, {[a[4]]}] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 2, a[6] = 0} The value of the game = , [ {f[1](a[1] - 1, 1, 0, 0, 2, 0), f[1](a[1], 0, 0, 0, 1, 1)}, {f[2](a[1], 0, 0, 0, 2) + [0]}] = , [{[{[4 a[1] - 1]}, {[4 a[1] - 1]}], [{[5 a[1]]}, {[4 a[1] - 1]}]}, {[4 a[1]]}] = , [4 a[1] - 1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0, a[5] = 2, a[6] = 0} The value of the game = , [{f[1](0, 0, 0, 0, 1, 1)}, {f[2](0, 0, 0, 0, 2) + [0]}] = , [{[{[0]}, {[-1]}]}, {[0]}] = , [-1] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 2, a[6] = 0} The value of the game = , [{f[1](a[1], a[2] - 1, 1, 0, 2, 0), f[1](a[1] - 1, a[2] + 1, 0, 0, 2, 0), f[1](a[1], a[2], 0, 0, 1, 1)}, {f[2](a[1], a[2], 0, 0, 2) + [0]}] = , [{[{[5 a[1] + 4 a[2]]}, {[%1, %1]}], [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}], [{[{[5 a[1] + 4 a[2] - 1]}, %1]}, {[4 a[1] + 3 a[2] - 1]}]}, %1] %1 := {[4 a[1] + 3 a[2]]} = , [{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, a[5] = 2, a[6] = 0} The value of the game = , [ {f[1](0, a[2] - 1, 1, 0, 2, 0), f[1](0, a[2], 0, 0, 1, 1)}, {f[2](0, a[2], 0, 0, 2) + [0]}] = , [{[{[4 a[2]]}, {[{[3 a[2]]}, {[3 a[2]]}]}], [{[{[-1 + 4 a[2]]}, {[3 a[2]]}]}, {[-1 + 3 a[2]]}]}, {[3 a[2]]}] = , [{[3 a[2]]}, {[3 a[2]]}] For the domain, { 1 <= a[2], 1 <= a[1], a[4] = 0, 1 <= a[3], a[5] = 2, a[6] = 0 } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], 0, 2, 0), f[1](a[1], a[2], a[3], 0, 1, 1), f[1](a[1], a[2] - 1, a[3] + 1, 0, 2, 0), f[1](a[1], a[2], a[3] - 1, 1, 2, 0)}, {f[2](a[1], a[2], a[3], 0, 2) + [0]}] = , [{[{[{[5 a[1] - 1 + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}]}, {[4 a[1] + 3 a[2] + 2 a[3] - 1]}], [ {[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}] = , [{[{[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}] For the domain, { a[2] = 0, 1 <= a[1], a[4] = 0, 1 <= a[3], a[5] = 2, a[6] = 0} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 1, 2, 0), f[1](a[1], 0, a[3], 0, 1, 1), f[1](a[1] - 1, 1, a[3], 0, 2, 0)}, {f[2](a[1], 0, a[3], 0, 2) + [0]}] = , [{[{[5 a[1] + 3 a[3]]}, {[4 a[1] + 1 + 2 a[3]]}], [ {[{[5 a[1] - 1 + 3 a[3]]}, {[4 a[1] + 2 a[3]]}]}, {[4 a[1] - 1 + 2 a[3]]}]}, {[4 a[1] + 2 a[3]]}] = , [{[{[5 a[1] + 3 a[3]]}, {[4 a[1] + 1 + 2 a[3]]}]}, {[4 a[1] + 2 a[3]]}] For the domain, { a[1] = 0, 1 <= a[2], a[4] = 0, 1 <= a[3], a[5] = 2, a[6] = 0} The value of the game = , [{f[1](0, a[2], a[3] - 1, 1, 2, 0), f[1](0, a[2] - 1, a[3] + 1, 0, 2, 0), f[1](0, a[2], a[3], 0, 1, 1)}, {f[2](0, a[2], a[3], 0, 2) + [0]}] = , [{[{[4 a[2] + 3 a[3]]}, {[1 + 3 a[2] + 2 a[3]]}], [ {[{[-1 + 4 a[2] + 3 a[3]]}, {[3 a[2] + 2 a[3]]}]}, {[-1 + 3 a[2] + 2 a[3]]}]}, {[3 a[2] + 2 a[3]]}] = , [{[{[4 a[2] + 3 a[3]]}, {[1 + 3 a[2] + 2 a[3]]}]}, {[3 a[2] + 2 a[3]]}] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, 1 <= a[3], a[5] = 2, a[6] = 0} The value of the game = , [ {f[1](0, 0, a[3], 0, 1, 1), f[1](0, 0, a[3] - 1, 1, 2, 0)}, {f[2](0, 0, a[3], 0, 2) + [0]}] = , [{[{[3 a[3]]}, {[1 + 2 a[3]]}], [{[{[-1 + 3 a[3]]}, {[2 a[3]]}]}, {[-1 + 2 a[3]]}]}, {[2 a[3]]}] = , [{[{[3 a[3]]}, {[1 + 2 a[3]]}]}, {[2 a[3]]}] For the domain, {1 <= a[2], 1 <= a[1], 1 <= a[3], 1 <= a[4], a[5] = 2, a[6] = 0} The value of the game = , [{ f[1](a[1], a[2] - 1, a[3] + 1, a[4], 2, 0), f[1](a[1] - 1, a[2] + 1, a[3], a[4], 2, 0), f[1](a[1], a[2], a[3], a[4] - 1, 3, 0), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 2, 0), f[1](a[1], a[2], a[3], a[4], 1, 1)}, {f[2](a[1], a[2], a[3], a[4], 2) + [0]}] = , [{[{[{[5 a[1] - 1 + 4 a[2] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}], [ {[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}] = , [{[{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], 1 <= a[4], a[5] = 2, a[6] = 0 } The value of the game = , [{f[1](a[1], a[2], 0, a[4], 1, 1), f[1](a[1], a[2], 0, a[4] - 1, 3, 0), f[1](a[1] - 1, a[2] + 1, 0, a[4], 2, 0), f[1](a[1], a[2] - 1, 1, a[4], 2, 0)}, {f[2](a[1], a[2], 0, a[4], 2) + [0]}] = , [{[{[ {[5 a[1] - 1 + 4 a[2] + 2 a[4]]}, {[4 a[1] + 3 a[2] + a[4]]}] }, {[4 a[1] + 3 a[2] - 1 + a[4]]}], [ {[5 a[1] + 4 a[2] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}] }, {[4 a[1] + 3 a[2] + a[4]]}] = , [{[ {[5 a[1] + 4 a[2] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}] }, {[4 a[1] + 3 a[2] + a[4]]}] For the domain, { a[2] = 0, 1 <= a[1], 1 <= a[3], 1 <= a[4], a[5] = 2, a[6] = 0 } The value of the game = , [{f[1](a[1], 0, a[3], a[4], 1, 1), f[1](a[1], 0, a[3] - 1, a[4] + 1, 2, 0), f[1](a[1], 0, a[3], a[4] - 1, 3, 0), f[1](a[1] - 1, 1, a[3], a[4], 2, 0)}, {f[2](a[1], 0, a[3], a[4], 2) + [0]}] = , [{[{[ {[5 a[1] - 1 + 3 a[3] + 2 a[4]]}, {[4 a[1] + 2 a[3] + a[4]]}] }, {[4 a[1] - 1 + 2 a[3] + a[4]]}], [ {[5 a[1] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}] }, {[4 a[1] + 2 a[3] + a[4]]}] = , [{[ {[5 a[1] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}] }, {[4 a[1] + 2 a[3] + a[4]]}] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[1], 1 <= a[4], a[5] = 2, a[6] = 0} The value of the game = , [{f[1](a[1] - 1, 1, 0, a[4], 2, 0), f[1](a[1], 0, 0, a[4] - 1, 3, 0), f[1](a[1], 0, 0, a[4], 1, 1)}, {f[2](a[1], 0, 0, a[4], 2) + [0]}] = , [{[{[{[5 a[1] - 1 + 2 a[4]]}, {[4 a[1] + a[4]]}]}, {[4 a[1] - 1 + a[4]]}], [{[5 a[1] + 2 a[4]]}, {[4 a[1] + 1 + a[4]]}]}, {[4 a[1] + a[4]]}] = , [{[{[5 a[1] + 2 a[4]]}, {[4 a[1] + 1 + a[4]]}]}, {[4 a[1] + a[4]]}] For the domain, { a[1] = 0, 1 <= a[2], 1 <= a[3], 1 <= a[4], a[5] = 2, a[6] = 0 } The value of the game = , [{ f[1](0, a[2], a[3] - 1, a[4] + 1, 2, 0), f[1](0, a[2], a[3], a[4] - 1, 3, 0), f[1](0, a[2] - 1, a[3] + 1, a[4], 2, 0), f[1](0, a[2], a[3], a[4], 1, 1)}, {f[2](0, a[2], a[3], a[4], 2) + [0]}] = , [{[{[ {[-1 + 4 a[2] + 3 a[3] + 2 a[4]]}, {[3 a[2] + 2 a[3] + a[4]]} ]}, {[-1 + 3 a[2] + 2 a[3] + a[4]]}], [ {[4 a[2] + 3 a[3] + 2 a[4]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] }, {[3 a[2] + 2 a[3] + a[4]]}] = , [{[ {[4 a[2] + 3 a[3] + 2 a[4]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] }, {[3 a[2] + 2 a[3] + a[4]]}] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], 1 <= a[4], a[5] = 2, a[6] = 0} The value of the game = , [{f[1](0, a[2], 0, a[4] - 1, 3, 0), f[1](0, a[2], 0, a[4], 1, 1), f[1](0, a[2] - 1, 1, a[4], 2, 0)}, {f[2](0, a[2], 0, a[4], 2) + [0]}] = , [{[{[{[-1 + 4 a[2] + 2 a[4]]}, {[3 a[2] + a[4]]}]}, {[-1 + 3 a[2] + a[4]]}], [{[4 a[2] + 2 a[4]]}, {[1 + 3 a[2] + a[4]]}]}, {[3 a[2] + a[4]]}] = , [{[{[4 a[2] + 2 a[4]]}, {[1 + 3 a[2] + a[4]]}]}, {[3 a[2] + a[4]]}] For the domain, { a[1] = 0, a[2] = 0, 1 <= a[3], 1 <= a[4], a[5] = 2, a[6] = 0} The value of the game = , [{f[1](0, 0, a[3], a[4], 1, 1), f[1](0, 0, a[3], a[4] - 1, 3, 0), f[1](0, 0, a[3] - 1, a[4] + 1, 2, 0)}, {f[2](0, 0, a[3], a[4], 2) + [0]}] = , [{[{[{[-1 + 3 a[3] + 2 a[4]]}, {[2 a[3] + a[4]]}]}, {[-1 + 2 a[3] + a[4]]}], [{[3 a[3] + 2 a[4]]}, {[1 + 2 a[3] + a[4]]}]}, {[2 a[3] + a[4]]}] = , [{[{[3 a[3] + 2 a[4]]}, {[1 + 2 a[3] + a[4]]}]}, {[2 a[3] + a[4]]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 1 <= a[4], a[5] = 2, a[6] = 0} The value of the game = , [ {f[1](0, 0, 0, a[4], 1, 1), f[1](0, 0, 0, a[4] - 1, 3, 0)}, {f[2](0, 0, 0, a[4], 2) + [0]}] = , [{[{[2 a[4]]}, {[a[4] + 1]}], [{[{[-1 + 2 a[4]]}, {[a[4]]}]}, {[a[4] - 1]}]}, {[a[4]]}] = , [{[{[2 a[4]]}, {[a[4] + 1]}]}, {[a[4]]}] For the domain, {1 <= a[2], 1 <= a[1], 1 <= a[3], 1 <= a[4], 3 <= a[5], a[6] = 0} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], a[5], 0), f[1](a[1], a[2], a[3] - 1, a[4] + 1, a[5], 0), f[1](a[1], a[2] - 1, a[3] + 1, a[4], a[5], 0), f[1](a[1], a[2], a[3], a[4], a[5] - 1, 1), f[1](a[1], a[2], a[3], a[4] - 1, a[5] + 1, 0)}, {f[2](a[1], a[2], a[3], a[4], a[5]) + [0]}] = , [{[{[{[5 a[1] - 3 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}], [ {[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}] = , [{[{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 0, 1 <= a[3], 3 <= a[5], a[6] = 0} The value of the game = , [{f[1](a[1], a[2], a[3], 0, a[5] - 1, 1), f[1](a[1], a[2] - 1, a[3] + 1, 0, a[5], 0), f[1](a[1], a[2], a[3] - 1, 1, a[5], 0), f[1](a[1] - 1, a[2] + 1, a[3], 0, a[5], 0)}, {f[2](a[1], a[2], a[3], 0, a[5]) + [0]}] = , [{[{[{[5 a[1] - 3 + 4 a[2] + 3 a[3] + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}]}, {[4 a[1] + 3 a[2] + 2 a[3] - 1]}], [ {[5 a[1] + 4 a[2] + 3 a[3] - 2 + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}] = , [{[{[5 a[1] + 4 a[2] + 3 a[3] - 2 + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], 1 <= a[4], 3 <= a[5], a[6] = 0} The value of the game = , [{f[1](a[1], a[2], 0, a[4], a[5] - 1, 1), f[1](a[1], a[2] - 1, 1, a[4], a[5], 0), f[1](a[1] - 1, a[2] + 1, 0, a[4], a[5], 0), f[1](a[1], a[2], 0, a[4] - 1, a[5] + 1, 0)}, {f[2](a[1], a[2], 0, a[4], a[5]) + [0]}] = , [{[{[5 a[1] + 4 a[2] - 2 + 2 a[4] + a[5]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}], [{[ {[5 a[1] - 3 + 4 a[2] + 2 a[4] + a[5]]}, {[4 a[1] + 3 a[2] + a[4]]}]}, {[4 a[1] + 3 a[2] - 1 + a[4]]}] }, {[4 a[1] + 3 a[2] + a[4]]}] = , [{[{[5 a[1] + 4 a[2] - 2 + 2 a[4] + a[5]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}]}, {[4 a[1] + 3 a[2] + a[4]]}] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, 3 <= a[5], a[6] = 0 } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, 0, 0, a[5], 0), f[1](a[1], a[2] - 1, 1, 0, a[5], 0), f[1](a[1], a[2], 0, 0, a[5] - 1, 1)}, {f[2](a[1], a[2], 0, 0, a[5]) + [0]}] = , [{[{[5 a[1] + 4 a[2] - 2 + a[5]]}, {[4 a[1] + 3 a[2] + 1]}], [ {[{[5 a[1] - 3 + 4 a[2] + a[5]]}, {[4 a[1] + 3 a[2]]}]}, {[4 a[1] + 3 a[2] - 1]}]}, {[4 a[1] + 3 a[2]]}] = , [{[{[5 a[1] + 4 a[2] - 2 + a[5]]}, {[4 a[1] + 3 a[2] + 1]}]}, {[4 a[1] + 3 a[2]]}] For the domain, {a[2] = 0, 1 <= a[1], 1 <= a[3], 1 <= a[4], 3 <= a[5], a[6] = 0} The value of the game = , [{ f[1](a[1], 0, a[3], a[4] - 1, a[5] + 1, 0), f[1](a[1], 0, a[3], a[4], a[5] - 1, 1), f[1](a[1], 0, a[3] - 1, a[4] + 1, a[5], 0), f[1](a[1] - 1, 1, a[3], a[4], a[5], 0)}, {f[2](a[1], 0, a[3], a[4], a[5]) + [0]}] = , [{[{[{[5 a[1] - 3 + 3 a[3] + 2 a[4] + a[5]]}, {[4 a[1] + 2 a[3] + a[4]]}]}, {[4 a[1] - 1 + 2 a[3] + a[4]]}] , [{[5 a[1] - 2 + 3 a[3] + 2 a[4] + a[5]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}]}, {[4 a[1] + 2 a[3] + a[4]]}] = , [{[{[5 a[1] - 2 + 3 a[3] + 2 a[4] + a[5]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}]}, {[4 a[1] + 2 a[3] + a[4]]}] For the domain, { a[2] = 0, 1 <= a[1], a[4] = 0, 1 <= a[3], 3 <= a[5], a[6] = 0 } The value of the game = , [{f[1](a[1] - 1, 1, a[3], 0, a[5], 0), f[1](a[1], 0, a[3] - 1, 1, a[5], 0), f[1](a[1], 0, a[3], 0, a[5] - 1, 1)}, {f[2](a[1], 0, a[3], 0, a[5]) + [0]}] = , [{[{[5 a[1] - 2 + 3 a[3] + a[5]]}, {[4 a[1] + 1 + 2 a[3]]}], [ {[{[5 a[1] - 3 + 3 a[3] + a[5]]}, {[4 a[1] + 2 a[3]]}]}, {[4 a[1] - 1 + 2 a[3]]}]}, {[4 a[1] + 2 a[3]]}] = , [{[{[5 a[1] - 2 + 3 a[3] + a[5]]}, {[4 a[1] + 1 + 2 a[3]]}]}, {[4 a[1] + 2 a[3]]}] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[1], 1 <= a[4], 3 <= a[5], a[6] = 0 } The value of the game = , [{ f[1](a[1], 0, 0, a[4] - 1, a[5] + 1, 0), f[1](a[1] - 1, 1, 0, a[4], a[5], 0), f[1](a[1], 0, 0, a[4], a[5] - 1, 1)}, {f[2](a[1], 0, 0, a[4], a[5]) + [0]}] = , [{[{[5 a[1] - 2 + 2 a[4] + a[5]]}, {[4 a[1] + 1 + a[4]]}], [ {[{[5 a[1] - 3 + 2 a[4] + a[5]]}, {[4 a[1] + a[4]]}]}, {[4 a[1] - 1 + a[4]]}]}, {[4 a[1] + a[4]]}] = , [{[{[5 a[1] - 2 + 2 a[4] + a[5]]}, {[4 a[1] + 1 + a[4]]}]}, {[4 a[1] + a[4]]}] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, 3 <= a[5], a[6] = 0} The value of the game = , [{f[1](a[1], 0, 0, 0, a[5] - 1, 1), f[1](a[1] - 1, 1, 0, 0, a[5], 0)}, {f[2](a[1], 0, 0, 0, a[5]) + [0]}] = , [{[{[5 a[1] - 2 + a[5]]}, {[4 a[1] + 1]}], [{[{[5 a[1] - 3 + a[5]]}, {[4 a[1]]}]}, {[4 a[1] - 1]}]}, {[4 a[1]]}] = , [{[{[5 a[1] - 2 + a[5]]}, {[4 a[1] + 1]}]}, {[4 a[1]]}] For the domain, {a[1] = 0, 1 <= a[2], 1 <= a[3], 1 <= a[4], 3 <= a[5], a[6] = 0} The value of the game = , [{ f[1](0, a[2], a[3], a[4] - 1, a[5] + 1, 0), f[1](0, a[2], a[3], a[4], a[5] - 1, 1), f[1](0, a[2] - 1, a[3] + 1, a[4], a[5], 0), f[1](0, a[2], a[3] - 1, a[4] + 1, a[5], 0)}, {f[2](0, a[2], a[3], a[4], a[5]) + [0]}] = , [{[{[{[-3 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {[3 a[2] + 2 a[3] + a[4]]}]}, {[-1 + 3 a[2] + 2 a[3] + a[4]]} ], [{[-2 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}]}, {[3 a[2] + 2 a[3] + a[4]]}] = , [{[{[-2 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}]}, {[3 a[2] + 2 a[3] + a[4]]}] For the domain, { a[1] = 0, 1 <= a[2], a[4] = 0, 1 <= a[3], 3 <= a[5], a[6] = 0 } The value of the game = , [{f[1](0, a[2], a[3] - 1, 1, a[5], 0), f[1](0, a[2] - 1, a[3] + 1, 0, a[5], 0), f[1](0, a[2], a[3], 0, a[5] - 1, 1)}, {f[2](0, a[2], a[3], 0, a[5]) + [0]}] = , [{[{[{[-3 + 4 a[2] + 3 a[3] + a[5]]}, {[3 a[2] + 2 a[3]]}]}, {[-1 + 3 a[2] + 2 a[3]]}], [{[-2 + 4 a[2] + 3 a[3] + a[5]]}, {[1 + 3 a[2] + 2 a[3]]}]}, {[3 a[2] + 2 a[3]]}] = , [{[{[-2 + 4 a[2] + 3 a[3] + a[5]]}, {[1 + 3 a[2] + 2 a[3]]}]}, {[3 a[2] + 2 a[3]]}] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], 1 <= a[4], 3 <= a[5], a[6] = 0 } The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], a[5], 0), f[1](0, a[2], 0, a[4], a[5] - 1, 1), f[1](0, a[2], 0, a[4] - 1, a[5] + 1, 0)}, {f[2](0, a[2], 0, a[4], a[5]) + [0]}] = , [{[{[{[-3 + 4 a[2] + 2 a[4] + a[5]]}, {[3 a[2] + a[4]]}]}, {[-1 + 3 a[2] + a[4]]}], [{[-2 + 4 a[2] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + a[4]]}]}, {[3 a[2] + a[4]]}] = , [{[{[-2 + 4 a[2] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + a[4]]}]}, {[3 a[2] + a[4]]}] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, 3 <= a[5], a[6] = 0} The value of the game = , [{f[1](0, a[2], 0, 0, a[5] - 1, 1), f[1](0, a[2] - 1, 1, 0, a[5], 0)}, {f[2](0, a[2], 0, 0, a[5]) + [0]}] = , [{[{[-2 + 4 a[2] + a[5]]}, {[1 + 3 a[2]]}], [{[{[-3 + 4 a[2] + a[5]]}, {[3 a[2]]}]}, {[-1 + 3 a[2]]}]}, {[3 a[2]]}] = , [{[{[-2 + 4 a[2] + a[5]]}, {[1 + 3 a[2]]}]}, {[3 a[2]]}] For the domain, { a[1] = 0, a[2] = 0, 1 <= a[3], 1 <= a[4], 3 <= a[5], a[6] = 0 } The value of the game = , [{ f[1](0, 0, a[3] - 1, a[4] + 1, a[5], 0), f[1](0, 0, a[3], a[4], a[5] - 1, 1), f[1](0, 0, a[3], a[4] - 1, a[5] + 1, 0)}, {f[2](0, 0, a[3], a[4], a[5]) + [0]}] = , [{[{[{[-3 + 3 a[3] + 2 a[4] + a[5]]}, {[2 a[3] + a[4]]}]}, {[-1 + 2 a[3] + a[4]]}], [{[-2 + 3 a[3] + 2 a[4] + a[5]]}, {[1 + 2 a[3] + a[4]]}]}, {[2 a[3] + a[4]]}] = , [{[{[-2 + 3 a[3] + 2 a[4] + 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, 1 <= a[3], 3 <= a[5], a[6] = 0} The value of the game = , [{f[1](0, 0, a[3], 0, a[5] - 1, 1), f[1](0, 0, a[3] - 1, 1, a[5], 0)}, {f[2](0, 0, a[3], 0, a[5]) + [0]}] = , [{[{[-2 + 3 a[3] + a[5]]}, {[1 + 2 a[3]]}], [{[{[-3 + 3 a[3] + a[5]]}, {[2 a[3]]}]}, {[-1 + 2 a[3]]}]}, {[2 a[3]]}] = , [{[{[-2 + 3 a[3] + a[5]]}, {[1 + 2 a[3]]}]}, {[2 a[3]]}] For the domain, { a[1] = 0, a[3] = 0, a[2] = 0, 1 <= a[4], 3 <= a[5], a[6] = 0} The value of the game = , [{f[1](0, 0, 0, a[4] - 1, a[5] + 1, 0), f[1](0, 0, 0, a[4], a[5] - 1, 1)}, {f[2](0, 0, 0, a[4], a[5]) + [0]}] = , [{[{[-2 + 2 a[4] + a[5]]}, {[a[4] + 1]}], [{[{[-3 + 2 a[4] + a[5]]}, {[a[4]]}]}, {[a[4] - 1]}]}, {[a[4]]}] = , [{[{[-2 + 2 a[4] + a[5]]}, {[a[4] + 1]}]}, {[a[4]]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0, 3 <= a[5], a[6] = 0} The value of the game = , [{f[1](0, 0, 0, 0, a[5] - 1, 1)}, {f[2](0, 0, 0, 0, a[5]) + [0]}] = , [{[{[-2 + a[5]]}, {[1]}]}, {[0]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{}, {f[2](0, 0, 0, 0, 0) + [1]}] = , [{}, {[-3]}] = , [-4] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](a[1] - 1, 1, 0, 0, 0, 1)}, {f[2](a[1], 0, 0, 0, 0) + [1]}] = , [{[4 a[1] - 3]}, {[4 a[1] - 3]}] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 0, 0, 1), f[1](a[1], a[2] - 1, 1, 0, 0, 1)}, {f[2](a[1], a[2], 0, 0, 0) + [1]}] = , [{[4 a[1] + 3 a[2] - 3]}, {[{[4 a[1] + 3 a[2] - 2]}, {[4 a[1] + 3 a[2] - 2]}]}] = , [4 a[1] + 3 a[2] - 2] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](0, a[2] - 1, 1, 0, 0, 1)}, {f[2](0, a[2], 0, 0, 0) + [1]}] = , [{[-3 + 3 a[2]]}, {[{[-2 + 3 a[2]]}, {[-2 + 3 a[2]]}]}] = , [-2 + 3 a[2]] For the domain, { 1 <= a[2], a[3] = 1, 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 1, 0, 0, 1), f[1](a[1], a[2], 0, 1, 0, 1), f[1](a[1], a[2] - 1, 2, 0, 0, 1)}, {f[2](a[1], a[2], 1, 0, 0) + [1]}] = , [{[{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}], [4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] + 1]}] = , [4 a[1] + 3 a[2]] For the domain, {a[2] = 0, a[3] = 1, 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [ {f[1](a[1], 0, 0, 1, 0, 1), f[1](a[1] - 1, 1, 1, 0, 0, 1)}, {f[2](a[1], 0, 1, 0, 0) + [1]}] = , [{[4 a[1] - 1]}, {[4 a[1] + 1]}] = , [4 a[1]] For the domain, {a[1] = 0, 1 <= a[2], a[3] = 1, a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [ {f[1](0, a[2] - 1, 2, 0, 0, 1), f[1](0, a[2], 0, 1, 0, 1)}, {f[2](0, a[2], 1, 0, 0) + [1]}] = , [{[{[3 a[2]]}, {[3 a[2]]}]}, {[3 a[2] + 1]}] = , [3 a[2]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 1, a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](0, 0, 0, 1, 0, 1)}, {f[2](0, 0, 1, 0, 0) + [1]}] = , [{[-1]}, {[1]}] = , [0] For the domain, { 1 <= a[2], 2 <= a[3], 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 1 } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], 0, 0, 1), f[1](a[1], a[2] - 1, a[3] + 1, 0, 0, 1), f[1](a[1], a[2], a[3] - 1, 1, 0, 1)}, {f[2](a[1], a[2], a[3], 0, 0) + [1]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 1], [ {[4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}]}, {[4 a[1] + 3 a[2] + 2 a[3] - 1]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] - 1]}] For the domain, { a[2] = 0, 2 <= a[3], 1 <= a[1], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 1, 0, 1), f[1](a[1] - 1, 1, a[3], 0, 0, 1)}, {f[2](a[1], 0, a[3], 0, 0) + [1]}] = , [{[{[4 a[1] - 2 + 2 a[3]]}, {[4 a[1] - 2 + 2 a[3]]}], [4 a[1] - 1 + 2 a[3]]}, {[4 a[1] - 1 + 2 a[3]]}] = , [{[4 a[1] - 1 + 2 a[3]]}, {[4 a[1] - 1 + 2 a[3]]}] For the domain, { a[1] = 0, 1 <= a[2], 2 <= a[3], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](0, a[2], a[3] - 1, 1, 0, 1), f[1](0, a[2] - 1, a[3] + 1, 0, 0, 1)}, {f[2](0, a[2], a[3], 0, 0) + [1]}] = , [{[{[-2 + 3 a[2] + 2 a[3]]}, {[-2 + 3 a[2] + 2 a[3]]}], [-1 + 3 a[2] + 2 a[3]]}, {[-1 + 3 a[2] + 2 a[3]]}] = , [{[-1 + 3 a[2] + 2 a[3]]}, {[-1 + 3 a[2] + 2 a[3]]}] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[3], a[4] = 0, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](0, 0, a[3] - 1, 1, 0, 1)}, {f[2](0, 0, a[3], 0, 0) + [1]}] = , [{[-1 + 2 a[3]]}, {[-1 + 2 a[3]]}] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 1, a[5] = 0, a[6] = 1} The value of the game = , [ {f[1](a[1], 0, 0, 0, 1, 1), f[1](a[1] - 1, 1, 0, 1, 0, 1)}, {f[2](a[1], 0, 0, 1, 0) + [1]}] = , [{[{[4 a[1] - 1]}, {[4 a[1] - 1]}], [{[5 a[1]]}, {[4 a[1] - 1]}]}, {[4 a[1]]}] = , [4 a[1] - 1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 1, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](0, 0, 0, 0, 1, 1)}, {f[2](0, 0, 0, 1, 0) + [1]}] = , [{[{[0]}, {[-1]}]}, {[0]}] = , [-1] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 1, a[5] = 0, a[6] = 1} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 1, 0, 1), f[1](a[1], a[2], 0, 0, 1, 1), f[1](a[1], a[2] - 1, 1, 1, 0, 1)}, {f[2](a[1], a[2], 0, 1, 0) + [1]}] = , [{%1, [{[5 a[1] + 4 a[2]]}, {[{%1}, {%1}]}], [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}]}, {%1}] %1 := [4 a[1] + 3 a[2]] = , [{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 1, a[5] = 0, a[6] = 1} The value of the game = , [ {f[1](0, a[2] - 1, 1, 1, 0, 1), f[1](0, a[2], 0, 0, 1, 1)}, {f[2](0, a[2], 0, 1, 0) + [1]}] = , [{[3 a[2]], [{[4 a[2]]}, {[{[3 a[2]]}, {[3 a[2]]}]}]}, {[3 a[2]]}] = , [{[3 a[2]]}, {[3 a[2]]}] For the domain, { 1 <= a[2], 1 <= a[1], a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 1 } The value of the game = , [{f[1](a[1], a[2], a[3] - 1, 2, 0, 1), f[1](a[1], a[2] - 1, a[3] + 1, 1, 0, 1), f[1](a[1] - 1, a[2] + 1, a[3], 1, 0, 1), f[1](a[1], a[2], a[3], 0, 1, 1)}, {f[2](a[1], a[2], a[3], 1, 0) + [1]}] = , [{[4 a[1] + 3 a[2] + 2 a[3]], [{[5 a[1] + 4 a[2] + 3 a[3]]}, %1]}, {[%1, %1]}] %1 := {[4 a[1] + 3 a[2] + 2 a[3] + 1]} = , [4 a[1] + 3 a[2] + 2 a[3] + 1] For the domain, { a[2] = 0, 1 <= a[1], a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{f[1](a[1], 0, a[3], 0, 1, 1), f[1](a[1] - 1, 1, a[3], 1, 0, 1), f[1](a[1], 0, a[3] - 1, 2, 0, 1)}, {f[2](a[1], 0, a[3], 1, 0) + [1]}] = , [{[4 a[1] + 2 a[3]], [{[5 a[1] + 3 a[3]]}, {[4 a[1] + 2 a[3] + 1]}]}, {[{[4 a[1] + 2 a[3] + 1]}, {[4 a[1] + 2 a[3] + 1]}]}] = , [4 a[1] + 2 a[3] + 1] For the domain, { a[1] = 0, 1 <= a[2], a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{f[1](0, a[2], a[3] - 1, 2, 0, 1), f[1](0, a[2], a[3], 0, 1, 1), f[1](0, a[2] - 1, a[3] + 1, 1, 0, 1)}, {f[2](0, a[2], a[3], 1, 0) + [1]}] = , [{[3 a[2] + 2 a[3]], [{[4 a[2] + 3 a[3]]}, {[3 a[2] + 2 a[3] + 1]}]}, {[{[3 a[2] + 2 a[3] + 1]}, {[3 a[2] + 2 a[3] + 1]}]}] = , [3 a[2] + 2 a[3] + 1] For the domain, {a[1] = 0, a[2] = 0, a[4] = 1, a[5] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [ {f[1](0, 0, a[3], 0, 1, 1), f[1](0, 0, a[3] - 1, 2, 0, 1)}, {f[2](0, 0, a[3], 1, 0) + [1]}] = , [{[2 a[3]], [{[3 a[3]]}, {[2 a[3] + 1]}]}, {[{[2 a[3] + 1]}, {[2 a[3] + 1]}]}] = , [2 a[3] + 1] For the domain, {1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{ f[1](a[1], a[2] - 1, a[3] + 1, a[4], 0, 1), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 0, 1), f[1](a[1], a[2], a[3], a[4] - 1, 1, 1), f[1](a[1] - 1, a[2] + 1, a[3], a[4], 0, 1)}, {f[2](a[1], a[2], a[3], a[4], 0) + [1]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1], [{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] - 2]}, %1]}, {[%1, %1]}] %1 := {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]} = , [4 a[1] + 3 a[2] + 2 a[3] + a[4]] For the domain, { a[3] = 0, 1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 0, a[6] = 1 } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, 0, a[4], 0, 1), f[1](a[1], a[2], 0, a[4] - 1, 1, 1), f[1](a[1], a[2] - 1, 1, a[4], 0, 1)}, {f[2](a[1], a[2], 0, a[4], 0) + [1]}] = , [{[4 a[1] + 3 a[2] - 1 + a[4]], [{[5 a[1] + 4 a[2] - 2 + 2 a[4]]}, %1]}, {[%1, %1]}] %1 := {[4 a[1] + 3 a[2] + a[4]]} = , [4 a[1] + 3 a[2] + a[4]] For the domain, { a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 0, 1 <= a[3], a[6] = 1 } The value of the game = , [{ f[1](a[1], 0, a[3] - 1, a[4] + 1, 0, 1), f[1](a[1] - 1, 1, a[3], a[4], 0, 1), f[1](a[1], 0, a[3], a[4] - 1, 1, 1)}, {f[2](a[1], 0, a[3], a[4], 0) + [1]}] = , [{[4 a[1] - 1 + 2 a[3] + a[4]], [{[5 a[1] - 2 + 3 a[3] + 2 a[4]]}, %1]}, {[%1, %1]}] %1 := {[4 a[1] + 2 a[3] + a[4]]} = , [4 a[1] + 2 a[3] + a[4]] For the domain, { a[3] = 0, a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 0, a[6] = 1} The value of the game = , [{f[1](a[1], 0, 0, a[4] - 1, 1, 1), f[1](a[1] - 1, 1, 0, a[4], 0, 1)}, {f[2](a[1], 0, 0, a[4], 0) + [1]}] = , [{[{[5 a[1] - 2 + 2 a[4]]}, {[4 a[1] + a[4]]}], [4 a[1] - 1 + a[4]]}, {[{[4 a[1] + a[4]]}, {[4 a[1] + a[4]]}]}] = , [4 a[1] + a[4]] For the domain, { a[1] = 0, 1 <= a[2], 2 <= a[4], a[5] = 0, 1 <= a[3], a[6] = 1 } The value of the game = , [{f[1](0, a[2], a[3], a[4] - 1, 1, 1), f[1](0, a[2], a[3] - 1, a[4] + 1, 0, 1), f[1](0, a[2] - 1, a[3] + 1, a[4], 0, 1)}, {f[2](0, a[2], a[3], a[4], 0) + [1]}] = , [{[-1 + 3 a[2] + 2 a[3] + a[4]], [{[-2 + 4 a[2] + 3 a[3] + 2 a[4]]}, %1]}, {[%1, %1]}] %1 := {[3 a[2] + 2 a[3] + a[4]]} = , [3 a[2] + 2 a[3] + a[4]] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[4], a[5] = 0, a[6] = 1} The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], 0, 1), f[1](0, a[2], 0, a[4] - 1, 1, 1)}, {f[2](0, a[2], 0, a[4], 0) + [1]}] = , [{[-1 + 3 a[2] + a[4]], [{[-2 + 4 a[2] + 2 a[4]]}, {[3 a[2] + a[4]]}]}, {[{[3 a[2] + a[4]]}, {[3 a[2] + a[4]]}]}] = , [3 a[2] + a[4]] For the domain, { a[1] = 0, a[2] = 0, 2 <= a[4], a[5] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{f[1](0, 0, a[3] - 1, a[4] + 1, 0, 1), f[1](0, 0, a[3], a[4] - 1, 1, 1)}, {f[2](0, 0, a[3], a[4], 0) + [1]}] = , [{[{[-2 + 3 a[3] + 2 a[4]]}, {[2 a[3] + a[4]]}], [-1 + 2 a[3] + a[4]]}, {[{[2 a[3] + a[4]]}, {[2 a[3] + a[4]]}]}] = , [2 a[3] + a[4]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 2 <= a[4], a[5] = 0, a[6] = 1} The value of the game = , [{f[1](0, 0, 0, a[4] - 1, 1, 1)}, {f[2](0, 0, 0, a[4], 0) + [1]}] = , [{[{[-2 + 2 a[4]]}, {[a[4]]}]}, {[{[a[4]]}, {[a[4]]}]}] = , [a[4]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 1} The value of the game = , [ {f[1](a[1] - 1, 1, 0, 0, 1, 1), f[1](a[1], 0, 0, 0, 0, 2)}, {f[2](a[1], 0, 0, 0, 1) + [1]}] = , [{[5 a[1]], [{[5 a[1] - 1]}, {[{[4 a[1] - 1]}, {[4 a[1] - 1]}]}]}, {[4 a[1] - 1]}] = , [{[5 a[1]]}, {[4 a[1] - 1]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 1, a[4] = 0, a[6] = 1} The value of the game = , [{f[1](0, 0, 0, 0, 0, 2)}, {f[2](0, 0, 0, 0, 1) + [1]}] = , [{[0]}, {[-1]}] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 0, a[6] = 1} The value of the game = , [{f[1](a[1] - 1, a[2] + 1, 0, 0, 1, 1), f[1](a[1], a[2] - 1, 1, 0, 1, 1), f[1](a[1], a[2], 0, 0, 0, 2)}, {f[2](a[1], a[2], 0, 0, 1) + [1]}] = , [{[{[5 a[1] - 1 + 4 a[2]]}, {[4 a[1] + 3 a[2]]}], [5 a[1] + 4 a[2]], [{[5 a[1] - 1 + 4 a[2]]}, {[{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}]}]}, {[{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}]}] = , [{[5 a[1] + 4 a[2]]}, {[{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 1, a[4] = 0, a[6] = 1} The value of the game = , [ {f[1](0, a[2], 0, 0, 0, 2), f[1](0, a[2] - 1, 1, 0, 1, 1)}, {f[2](0, a[2], 0, 0, 1) + [1]}] = , [{[{[-1 + 4 a[2]]}, {[3 a[2]]}], [4 a[2]]}, {[{[3 a[2]]}, {[3 a[2]]}]}] = , [{[4 a[2]]}, {[{[3 a[2]]}, {[3 a[2]]}]}] For the domain, { 1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 0, 1 <= a[3], a[6] = 1 } The value of the game = , [{ f[1](a[1], a[2] - 1, a[3] + 1, 0, 1, 1), f[1](a[1] - 1, a[2] + 1, a[3], 0, 1, 1), f[1](a[1], a[2], a[3], 0, 0, 2), f[1](a[1], a[2], a[3] - 1, 1, 1, 1)}, {f[2](a[1], a[2], a[3], 0, 1) + [1]}] = , [{[5 a[1] + 4 a[2] + 3 a[3]], [ {[5 a[1] - 1 + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}] = , [{[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}] For the domain, { a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 1, 1, 1), f[1](a[1], 0, a[3], 0, 0, 2), f[1](a[1] - 1, 1, a[3], 0, 1, 1)}, {f[2](a[1], 0, a[3], 0, 1) + [1]}] = , [{[5 a[1] + 3 a[3]], [{[5 a[1] - 1 + 3 a[3]]}, {[4 a[1] + 2 a[3]]}]}, {[4 a[1] + 1 + 2 a[3]]}] = , [{[5 a[1] + 3 a[3]]}, {[4 a[1] + 1 + 2 a[3]]}] For the domain, { a[1] = 0, 1 <= a[2], a[5] = 1, a[4] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{f[1](0, a[2], a[3] - 1, 1, 1, 1), f[1](0, a[2], a[3], 0, 0, 2), f[1](0, a[2] - 1, a[3] + 1, 0, 1, 1)}, {f[2](0, a[2], a[3], 0, 1) + [1]}] = , [{[4 a[2] + 3 a[3]], [{[-1 + 4 a[2] + 3 a[3]]}, {[3 a[2] + 2 a[3]]}]}, {[1 + 3 a[2] + 2 a[3]]}] = , [{[4 a[2] + 3 a[3]]}, {[1 + 3 a[2] + 2 a[3]]}] For the domain, {a[1] = 0, a[2] = 0, a[5] = 1, a[4] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [ {f[1](0, 0, a[3], 0, 0, 2), f[1](0, 0, a[3] - 1, 1, 1, 1)}, {f[2](0, 0, a[3], 0, 1) + [1]}] = , [{[{[-1 + 3 a[3]]}, {[2 a[3]]}], [3 a[3]]}, {[1 + 2 a[3]]}] = , [{[3 a[3]]}, {[1 + 2 a[3]]}] For the domain, {1 <= a[2], 1 <= a[1], a[5] = 1, 1 <= a[3], 1 <= a[4], a[6] = 1} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], 1, 1), f[1](a[1], a[2] - 1, a[3] + 1, a[4], 1, 1), f[1](a[1], a[2], a[3], a[4] - 1, 2, 1), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 1, 1), f[1](a[1], a[2], a[3], a[4], 0, 2)}, {f[2](a[1], a[2], a[3], a[4], 1) + [1]}] = , [{[{[5 a[1] - 1 + 4 a[2] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}], [5 a[1] + 4 a[2] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}] = , [{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 1, 1 <= a[4], a[6] = 1 } The value of the game = , [{f[1](a[1], a[2], 0, a[4], 0, 2), f[1](a[1], a[2], 0, a[4] - 1, 2, 1), f[1](a[1], a[2] - 1, 1, a[4], 1, 1), f[1](a[1] - 1, a[2] + 1, 0, a[4], 1, 1)}, {f[2](a[1], a[2], 0, a[4], 1) + [1]}] = , [{[ {[5 a[1] - 1 + 4 a[2] + 2 a[4]]}, {[4 a[1] + 3 a[2] + a[4]]}] , [5 a[1] + 4 a[2] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]} ] = , [{[5 a[1] + 4 a[2] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}] For the domain, { a[2] = 0, 1 <= a[1], a[5] = 1, 1 <= a[3], 1 <= a[4], a[6] = 1 } The value of the game = , [{f[1](a[1], 0, a[3], a[4], 0, 2), f[1](a[1], 0, a[3] - 1, a[4] + 1, 1, 1), f[1](a[1], 0, a[3], a[4] - 1, 2, 1), f[1](a[1] - 1, 1, a[3], a[4], 1, 1)}, {f[2](a[1], 0, a[3], a[4], 1) + [1]}] = , [{[5 a[1] + 3 a[3] + 2 a[4]], [ {[5 a[1] - 1 + 3 a[3] + 2 a[4]]}, {[4 a[1] + 2 a[3] + a[4]]}] }, {[4 a[1] + 1 + 2 a[3] + a[4]]}] = , [{[5 a[1] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 1, 1 <= a[4], a[6] = 1} The value of the game = , [{f[1](a[1] - 1, 1, 0, a[4], 1, 1), f[1](a[1], 0, 0, a[4] - 1, 2, 1), f[1](a[1], 0, 0, a[4], 0, 2)}, {f[2](a[1], 0, 0, a[4], 1) + [1]}] = , [{[{[5 a[1] - 1 + 2 a[4]]}, {[4 a[1] + a[4]]}], [5 a[1] + 2 a[4]]}, {[4 a[1] + 1 + a[4]]}] = , [{[5 a[1] + 2 a[4]]}, {[4 a[1] + 1 + a[4]]}] For the domain, { a[1] = 0, 1 <= a[2], a[5] = 1, 1 <= a[3], 1 <= a[4], a[6] = 1 } The value of the game = , [{f[1](0, a[2], a[3], a[4], 0, 2), f[1](0, a[2], a[3] - 1, a[4] + 1, 1, 1), f[1](0, a[2], a[3], a[4] - 1, 2, 1), f[1](0, a[2] - 1, a[3] + 1, a[4], 1, 1)}, {f[2](0, a[2], a[3], a[4], 1) + [1]}] = , [{[ {[-1 + 4 a[2] + 3 a[3] + 2 a[4]]}, {[3 a[2] + 2 a[3] + a[4]]} ], [4 a[2] + 3 a[3] + 2 a[4]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] = , [{[4 a[2] + 3 a[3] + 2 a[4]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 1, 1 <= a[4], a[6] = 1} The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], 1, 1), f[1](0, a[2], 0, a[4] - 1, 2, 1), f[1](0, a[2], 0, a[4], 0, 2)}, {f[2](0, a[2], 0, a[4], 1) + [1]}] = , [{[{[-1 + 4 a[2] + 2 a[4]]}, {[3 a[2] + a[4]]}], [4 a[2] + 2 a[4]]}, {[1 + 3 a[2] + a[4]]}] = , [{[4 a[2] + 2 a[4]]}, {[1 + 3 a[2] + a[4]]}] For the domain, { a[1] = 0, a[2] = 0, a[5] = 1, 1 <= a[3], 1 <= a[4], a[6] = 1} The value of the game = , [{f[1](0, 0, a[3], a[4] - 1, 2, 1), f[1](0, 0, a[3] - 1, a[4] + 1, 1, 1), f[1](0, 0, a[3], a[4], 0, 2)}, {f[2](0, 0, a[3], a[4], 1) + [1]}] = , [{[{[-1 + 3 a[3] + 2 a[4]]}, {[2 a[3] + a[4]]}], [3 a[3] + 2 a[4]]}, {[1 + 2 a[3] + a[4]]}] = , [{[3 a[3] + 2 a[4]]}, {[1 + 2 a[3] + a[4]]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 1, 1 <= a[4], a[6] = 1} The value of the game = , [ {f[1](0, 0, 0, a[4], 0, 2), f[1](0, 0, 0, a[4] - 1, 2, 1)}, {f[2](0, 0, 0, a[4], 1) + [1]}] = , [{[2 a[4]], [{[-1 + 2 a[4]]}, {[a[4]]}]}, {[a[4] + 1]}] = , [{[2 a[4]]}, {[a[4] + 1]}] For the domain, {2 <= a[5], 1 <= a[2], 1 <= a[1], 1 <= a[3], 1 <= a[4], a[6] = 1} The value of the game = , [{ f[1](a[1], a[2] - 1, a[3] + 1, a[4], a[5], 1), f[1](a[1] - 1, a[2] + 1, a[3], a[4], a[5], 1), f[1](a[1], a[2], a[3] - 1, a[4] + 1, a[5], 1), f[1](a[1], a[2], a[3], a[4], a[5] - 1, 2), f[1](a[1], a[2], a[3], a[4] - 1, a[5] + 1, 1)}, {f[2](a[1], a[2], a[3], a[4], a[5]) + [1]}] = , [{[{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}], [5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}] = , [{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}] For the domain, {2 <= a[5], 1 <= a[2], 1 <= a[1], a[4] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{f[1](a[1], a[2], a[3], 0, a[5] - 1, 2), f[1](a[1], a[2], a[3] - 1, 1, a[5], 1), f[1](a[1] - 1, a[2] + 1, a[3], 0, a[5], 1), f[1](a[1], a[2] - 1, a[3] + 1, 0, a[5], 1)}, {f[2](a[1], a[2], a[3], 0, a[5]) + [1]}] = , [{[{[5 a[1] + 4 a[2] + 3 a[3] - 2 + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}], [5 a[1] + 4 a[2] + 3 a[3] - 1 + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}] = , [{[5 a[1] + 4 a[2] + 3 a[3] - 1 + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}] For the domain, {a[3] = 0, 2 <= a[5], 1 <= a[2], 1 <= a[1], 1 <= a[4], a[6] = 1} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, 0, a[4], a[5], 1), f[1](a[1], a[2] - 1, 1, a[4], a[5], 1), f[1](a[1], a[2], 0, a[4] - 1, a[5] + 1, 1), f[1](a[1], a[2], 0, a[4], a[5] - 1, 2)}, {f[2](a[1], a[2], 0, a[4], a[5]) + [1]}] = , [{[5 a[1] + 4 a[2] - 1 + 2 a[4] + a[5]], [ {[5 a[1] + 4 a[2] - 2 + 2 a[4] + a[5]]}, {[4 a[1] + 3 a[2] + a[4]]}]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}] = , [{[5 a[1] + 4 a[2] - 1 + 2 a[4] + a[5]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}] For the domain, { a[3] = 0, 2 <= a[5], 1 <= a[2], 1 <= a[1], a[4] = 0, a[6] = 1 } The value of the game = , [{f[1](a[1], a[2], 0, 0, a[5] - 1, 2), f[1](a[1], a[2] - 1, 1, 0, a[5], 1), f[1](a[1] - 1, a[2] + 1, 0, 0, a[5], 1)}, {f[2](a[1], a[2], 0, 0, a[5]) + [1]}] = , [{[5 a[1] + 4 a[2] - 1 + a[5]], [{[5 a[1] + 4 a[2] - 2 + a[5]]}, {[4 a[1] + 3 a[2]]}]}, {[4 a[1] + 3 a[2] + 1]}] = , [{[5 a[1] + 4 a[2] - 1 + a[5]]}, {[4 a[1] + 3 a[2] + 1]}] For the domain, {a[2] = 0, 2 <= a[5], 1 <= a[1], 1 <= a[3], 1 <= a[4], a[6] = 1} The value of the game = , [{ f[1](a[1], 0, a[3], a[4] - 1, a[5] + 1, 1), f[1](a[1], 0, a[3], a[4], a[5] - 1, 2), f[1](a[1], 0, a[3] - 1, a[4] + 1, a[5], 1), f[1](a[1] - 1, 1, a[3], a[4], a[5], 1)}, {f[2](a[1], 0, a[3], a[4], a[5]) + [1]}] = , [{[5 a[1] - 1 + 3 a[3] + 2 a[4] + a[5]], [ {[5 a[1] - 2 + 3 a[3] + 2 a[4] + a[5]]}, {[4 a[1] + 2 a[3] + a[4]]}]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}] = , [{[5 a[1] - 1 + 3 a[3] + 2 a[4] + a[5]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}] For the domain, { a[2] = 0, 2 <= a[5], 1 <= a[1], a[4] = 0, 1 <= a[3], a[6] = 1 } The value of the game = , [{f[1](a[1] - 1, 1, a[3], 0, a[5], 1), f[1](a[1], 0, a[3] - 1, 1, a[5], 1), f[1](a[1], 0, a[3], 0, a[5] - 1, 2)}, {f[2](a[1], 0, a[3], 0, a[5]) + [1]}] = , [{[{[5 a[1] - 2 + 3 a[3] + a[5]]}, {[4 a[1] + 2 a[3]]}], [5 a[1] - 1 + 3 a[3] + a[5]]}, {[4 a[1] + 1 + 2 a[3]]}] = , [{[5 a[1] - 1 + 3 a[3] + a[5]]}, {[4 a[1] + 1 + 2 a[3]]}] For the domain, { a[3] = 0, a[2] = 0, 2 <= a[5], 1 <= a[1], 1 <= a[4], a[6] = 1 } The value of the game = , [{f[1](a[1], 0, 0, a[4], a[5] - 1, 2), f[1](a[1], 0, 0, a[4] - 1, a[5] + 1, 1), f[1](a[1] - 1, 1, 0, a[4], a[5], 1)}, {f[2](a[1], 0, 0, a[4], a[5]) + [1]}] = , [{[5 a[1] - 1 + 2 a[4] + a[5]], [{[5 a[1] - 2 + 2 a[4] + a[5]]}, {[4 a[1] + a[4]]}]}, {[4 a[1] + 1 + a[4]]}] = , [{[5 a[1] - 1 + 2 a[4] + a[5]]}, {[4 a[1] + 1 + a[4]]}] For the domain, { a[3] = 0, a[2] = 0, 2 <= a[5], 1 <= a[1], a[4] = 0, a[6] = 1} The value of the game = , [{f[1](a[1] - 1, 1, 0, 0, a[5], 1), f[1](a[1], 0, 0, 0, a[5] - 1, 2)}, {f[2](a[1], 0, 0, 0, a[5]) + [1]}] = , [{[5 a[1] - 1 + a[5]], [{[5 a[1] - 2 + a[5]]}, {[4 a[1]]}]}, {[4 a[1] + 1]}] = , [{[5 a[1] - 1 + a[5]]}, {[4 a[1] + 1]}] For the domain, {a[1] = 0, 2 <= a[5], 1 <= a[2], 1 <= a[3], 1 <= a[4], a[6] = 1} The value of the game = , [{ f[1](0, a[2], a[3], a[4] - 1, a[5] + 1, 1), f[1](0, a[2], a[3], a[4], a[5] - 1, 2), f[1](0, a[2], a[3] - 1, a[4] + 1, a[5], 1), f[1](0, a[2] - 1, a[3] + 1, a[4], a[5], 1)}, {f[2](0, a[2], a[3], a[4], a[5]) + [1]}] = , [{[-1 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]], [ {[-2 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {[3 a[2] + 2 a[3] + a[4]]}]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] = , [{[-1 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] For the domain, { a[1] = 0, 2 <= a[5], 1 <= a[2], a[4] = 0, 1 <= a[3], a[6] = 1 } The value of the game = , [{ f[1](0, a[2] - 1, a[3] + 1, 0, a[5], 1), f[1](0, a[2], a[3] - 1, 1, a[5], 1), f[1](0, a[2], a[3], 0, a[5] - 1, 2)}, {f[2](0, a[2], a[3], 0, a[5]) + [1]}] = , [{[{[-2 + 4 a[2] + 3 a[3] + a[5]]}, {[3 a[2] + 2 a[3]]}], [-1 + 4 a[2] + 3 a[3] + a[5]]}, {[1 + 3 a[2] + 2 a[3]]}] = , [{[-1 + 4 a[2] + 3 a[3] + a[5]]}, {[1 + 3 a[2] + 2 a[3]]}] For the domain, { a[1] = 0, a[3] = 0, 2 <= a[5], 1 <= a[2], 1 <= a[4], a[6] = 1 } The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], a[5], 1), f[1](0, a[2], 0, a[4], a[5] - 1, 2), f[1](0, a[2], 0, a[4] - 1, a[5] + 1, 1)}, {f[2](0, a[2], 0, a[4], a[5]) + [1]}] = , [{[-1 + 4 a[2] + 2 a[4] + a[5]], [{[-2 + 4 a[2] + 2 a[4] + a[5]]}, {[3 a[2] + a[4]]}]}, {[1 + 3 a[2] + a[4]]}] = , [{[-1 + 4 a[2] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + a[4]]}] For the domain, { a[1] = 0, a[3] = 0, 2 <= a[5], 1 <= a[2], a[4] = 0, a[6] = 1} The value of the game = , [{f[1](0, a[2], 0, 0, a[5] - 1, 2), f[1](0, a[2] - 1, 1, 0, a[5], 1)}, {f[2](0, a[2], 0, 0, a[5]) + [1]}] = , [{[-1 + 4 a[2] + a[5]], [{[-2 + 4 a[2] + a[5]]}, {[3 a[2]]}]}, {[1 + 3 a[2]]}] = , [{[-1 + 4 a[2] + a[5]]}, {[1 + 3 a[2]]}] For the domain, { a[1] = 0, a[2] = 0, 2 <= a[5], 1 <= a[3], 1 <= a[4], a[6] = 1 } The value of the game = , [{ f[1](0, 0, a[3] - 1, a[4] + 1, a[5], 1), f[1](0, 0, a[3], a[4], a[5] - 1, 2), f[1](0, 0, a[3], a[4] - 1, a[5] + 1, 1)}, {f[2](0, 0, a[3], a[4], a[5]) + [1]}] = , [{[-1 + 3 a[3] + 2 a[4] + a[5]], [{[-2 + 3 a[3] + 2 a[4] + a[5]]}, {[2 a[3] + a[4]]}]}, {[1 + 2 a[3] + a[4]]}] = , [{[-1 + 3 a[3] + 2 a[4] + a[5]]}, {[1 + 2 a[3] + a[4]]}] For the domain, { a[1] = 0, a[2] = 0, 2 <= a[5], a[4] = 0, 1 <= a[3], a[6] = 1} The value of the game = , [{f[1](0, 0, a[3], 0, a[5] - 1, 2), f[1](0, 0, a[3] - 1, 1, a[5], 1)}, {f[2](0, 0, a[3], 0, a[5]) + [1]}] = , [{[{[-2 + 3 a[3] + a[5]]}, {[2 a[3]]}], [-1 + 3 a[3] + a[5]]}, {[1 + 2 a[3]]}] = , [{[-1 + 3 a[3] + a[5]]}, {[1 + 2 a[3]]}] For the domain, { a[1] = 0, a[3] = 0, a[2] = 0, 2 <= a[5], 1 <= a[4], a[6] = 1} The value of the game = , [{f[1](0, 0, 0, a[4] - 1, a[5] + 1, 1), f[1](0, 0, 0, a[4], a[5] - 1, 2)}, {f[2](0, 0, 0, a[4], a[5]) + [1]}] = , [{[-1 + 2 a[4] + a[5]], [{[-2 + 2 a[4] + a[5]]}, {[a[4]]}]}, {[a[4] + 1]}] = , [{[-1 + 2 a[4] + a[5]]}, {[a[4] + 1]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 2 <= a[5], a[4] = 0, a[6] = 1} The value of the game = , [{f[1](0, 0, 0, 0, a[5] - 1, 2)}, {f[2](0, 0, 0, 0, a[5]) + [1]}] = , [{[a[5] - 1]}, {[1]}] For the domain, {1 <= a[2], 1 <= a[5], 1 <= a[1], 1 <= a[3], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](a[1], a[2] - 1, a[3] + 1, a[4], a[5], a[6]), f[1](a[1], a[2], a[3], a[4] - 1, a[5] + 1, a[6]), f[1](a[1], a[2], a[3] - 1, a[4] + 1, a[5], a[6]), f[1](a[1], a[2], a[3], a[4], a[5] - 1, a[6] + 1), f[1](a[1] - 1, a[2] + 1, a[3], a[4], a[5], a[6])}, {}] = , [{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 1]}, {}] = , [5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5]] For the domain, {1 <= a[2], 1 <= a[1], a[5] = 0, 1 <= a[3], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], a[4], 0, a[6]), f[1](a[1], a[2], a[3] - 1, a[4] + 1, 0, a[6]), f[1](a[1], a[2], a[3], a[4] - 1, 1, a[6]), f[1](a[1], a[2] - 1, a[3] + 1, a[4], 0, a[6])}, {}] = , [{[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] - 1]}, {}] = , [5 a[1] + 4 a[2] + 3 a[3] + 2 a[4]] For the domain, {1 <= a[2], 1 <= a[5], 1 <= a[1], a[4] = 0, 1 <= a[3], 2 <= a[6]} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, a[3], 0, a[5], a[6]), f[1](a[1], a[2], a[3], 0, a[5] - 1, a[6] + 1), f[1](a[1], a[2], a[3] - 1, 1, a[5], a[6]), f[1](a[1], a[2] - 1, a[3] + 1, 0, a[5], a[6])}, {}] = , [{[5 a[1] + 4 a[2] + 3 a[3] - 1 + a[5]]}, {}] = , [5 a[1] + 4 a[2] + 3 a[3] + a[5]] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 0, 1 <= a[3], 2 <= a[6]} The value of the game = , [{ f[1](a[1], a[2] - 1, a[3] + 1, 0, 0, a[6]), f[1](a[1], a[2], a[3] - 1, 1, 0, a[6]), f[1](a[1] - 1, a[2] + 1, a[3], 0, 0, a[6])}, {}] = , [{[5 a[1] + 4 a[2] + 3 a[3] - 1]}, {}] = , [5 a[1] + 4 a[2] + 3 a[3]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[5], 1 <= a[1], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, 0, a[4], a[5], a[6]), f[1](a[1], a[2], 0, a[4], a[5] - 1, a[6] + 1), f[1](a[1], a[2], 0, a[4] - 1, a[5] + 1, a[6]), f[1](a[1], a[2] - 1, 1, a[4], a[5], a[6])}, {}] = , [{[5 a[1] + 4 a[2] - 1 + 2 a[4] + a[5]]}, {}] = , [5 a[1] + 4 a[2] + 2 a[4] + a[5]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 0, 1 <= a[4], 2 <= a[6]} The value of the game = , [{f[1](a[1], a[2] - 1, 1, a[4], 0, a[6]), f[1](a[1], a[2], 0, a[4] - 1, 1, a[6]), f[1](a[1] - 1, a[2] + 1, 0, a[4], 0, a[6])}, {}] = , [{[5 a[1] + 4 a[2] - 1 + 2 a[4]]}, {}] = , [5 a[1] + 4 a[2] + 2 a[4]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[5], 1 <= a[1], a[4] = 0, 2 <= a[6]} The value of the game = , [{f[1](a[1], a[2] - 1, 1, 0, a[5], a[6]), f[1](a[1], a[2], 0, 0, a[5] - 1, a[6] + 1), f[1](a[1] - 1, a[2] + 1, 0, 0, a[5], a[6])}, {}] = , [{[5 a[1] + 4 a[2] - 1 + a[5]]}, {}] = , [5 a[1] + 4 a[2] + a[5]] For the domain, { a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 0, 2 <= a[6] } The value of the game = , [{ f[1](a[1] - 1, a[2] + 1, 0, 0, 0, a[6]), f[1](a[1], a[2] - 1, 1, 0, 0, a[6])}, {}] = , [{[5 a[1] + 4 a[2] - 1]}, {}] = , [5 a[1] + 4 a[2]] For the domain, {a[2] = 0, 1 <= a[5], 1 <= a[1], 1 <= a[3], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](a[1] - 1, 1, a[3], a[4], a[5], a[6]), f[1](a[1], 0, a[3], a[4], a[5] - 1, a[6] + 1), f[1](a[1], 0, a[3] - 1, a[4] + 1, a[5], a[6]), f[1](a[1], 0, a[3], a[4] - 1, a[5] + 1, a[6])}, {}] = , [{[5 a[1] - 1 + 3 a[3] + 2 a[4] + a[5]]}, {}] = , [5 a[1] + 3 a[3] + 2 a[4] + a[5]] For the domain, {a[2] = 0, 1 <= a[1], a[5] = 0, 1 <= a[3], 1 <= a[4], 2 <= a[6]} The value of the game = , [{f[1](a[1], 0, a[3], a[4] - 1, 1, a[6]), f[1](a[1], 0, a[3] - 1, a[4] + 1, 0, a[6]), f[1](a[1] - 1, 1, a[3], a[4], 0, a[6])}, {}] = , [{[5 a[1] - 1 + 3 a[3] + 2 a[4]]}, {}] = , [5 a[1] + 3 a[3] + 2 a[4]] For the domain, {a[2] = 0, 1 <= a[5], 1 <= a[1], a[4] = 0, 1 <= a[3], 2 <= a[6]} The value of the game = , [{f[1](a[1], 0, a[3] - 1, 1, a[5], a[6]), f[1](a[1], 0, a[3], 0, a[5] - 1, a[6] + 1), f[1](a[1] - 1, 1, a[3], 0, a[5], a[6])}, {}] = , [{[5 a[1] - 1 + 3 a[3] + a[5]]}, {}] = , [5 a[1] + 3 a[3] + a[5]] For the domain, { a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 0, 1 <= a[3], 2 <= a[6] } The value of the game = , [{f[1](a[1] - 1, 1, a[3], 0, 0, a[6]), f[1](a[1], 0, a[3] - 1, 1, 0, a[6])}, {}] = , [{[5 a[1] - 1 + 3 a[3]]}, {}] = , [5 a[1] + 3 a[3]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[5], 1 <= a[1], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](a[1], 0, 0, a[4] - 1, a[5] + 1, a[6]), f[1](a[1], 0, 0, a[4], a[5] - 1, a[6] + 1), f[1](a[1] - 1, 1, 0, a[4], a[5], a[6])}, {}] = , [{[5 a[1] - 1 + 2 a[4] + a[5]]}, {}] = , [5 a[1] + 2 a[4] + a[5]] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 0, 1 <= a[4], 2 <= a[6] } The value of the game = , [{f[1](a[1] - 1, 1, 0, a[4], 0, a[6]), f[1](a[1], 0, 0, a[4] - 1, 1, a[6])}, {}] = , [{[5 a[1] - 1 + 2 a[4]]}, {}] = , [5 a[1] + 2 a[4]] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[5], 1 <= a[1], a[4] = 0, 2 <= a[6] } The value of the game = , [{f[1](a[1] - 1, 1, 0, 0, a[5], a[6]), f[1](a[1], 0, 0, 0, a[5] - 1, a[6] + 1)}, {}] = , [{[5 a[1] - 1 + a[5]]}, {}] = , [5 a[1] + a[5]] For the domain, { a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 0, 2 <= a[6]} The value of the game = , [{f[1](a[1] - 1, 1, 0, 0, 0, a[6])}, {}] = , [{[5 a[1] - 1]}, {}] = , [5 a[1]] For the domain, {a[1] = 0, 1 <= a[2], 1 <= a[5], 1 <= a[3], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](0, a[2], a[3], a[4], a[5] - 1, a[6] + 1), f[1](0, a[2], a[3] - 1, a[4] + 1, a[5], a[6]), f[1](0, a[2], a[3], a[4] - 1, a[5] + 1, a[6]), f[1](0, a[2] - 1, a[3] + 1, a[4], a[5], a[6])}, {}] = , [{[-1 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {}] = , [4 a[2] + 3 a[3] + 2 a[4] + a[5]] For the domain, {a[1] = 0, 1 <= a[2], a[5] = 0, 1 <= a[3], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](0, a[2] - 1, a[3] + 1, a[4], 0, a[6]), f[1](0, a[2], a[3], a[4] - 1, 1, a[6]), f[1](0, a[2], a[3] - 1, a[4] + 1, 0, a[6])}, {}] = , [{[-1 + 4 a[2] + 3 a[3] + 2 a[4]]}, {}] = , [4 a[2] + 3 a[3] + 2 a[4]] For the domain, {a[1] = 0, 1 <= a[2], 1 <= a[5], a[4] = 0, 1 <= a[3], 2 <= a[6]} The value of the game = , [{ f[1](0, a[2] - 1, a[3] + 1, 0, a[5], a[6]), f[1](0, a[2], a[3] - 1, 1, a[5], a[6]), f[1](0, a[2], a[3], 0, a[5] - 1, a[6] + 1)}, {}] = , [{[-1 + 4 a[2] + 3 a[3] + a[5]]}, {}] = , [4 a[2] + 3 a[3] + a[5]] For the domain, { a[1] = 0, 1 <= a[2], a[4] = 0, a[5] = 0, 1 <= a[3], 2 <= a[6] } The value of the game = , [{ f[1](0, a[2] - 1, a[3] + 1, 0, 0, a[6]), f[1](0, a[2], a[3] - 1, 1, 0, a[6])}, {}] = , [{[-1 + 4 a[2] + 3 a[3]]}, {}] = , [4 a[2] + 3 a[3]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 1 <= a[5], 1 <= a[4], 2 <= a[6]} The value of the game = , [{f[1](0, a[2] - 1, 1, a[4], a[5], a[6]), f[1](0, a[2], 0, a[4] - 1, a[5] + 1, a[6]), f[1](0, a[2], 0, a[4], a[5] - 1, a[6] + 1)}, {}] = , [{[-1 + 4 a[2] + 2 a[4] + a[5]]}, {}] = , [4 a[2] + 2 a[4] + a[5]] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 0, 1 <= a[4], 2 <= a[6] } The value of the game = , [{f[1](0, a[2], 0, a[4] - 1, 1, a[6]), f[1](0, a[2] - 1, 1, a[4], 0, a[6])}, {}] = , [{[-1 + 4 a[2] + 2 a[4]]}, {}] = , [4 a[2] + 2 a[4]] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], 1 <= a[5], a[4] = 0, 2 <= a[6] } The value of the game = , [{ f[1](0, a[2], 0, 0, a[5] - 1, a[6] + 1), f[1](0, a[2] - 1, 1, 0, a[5], a[6])}, {}] = , [{[-1 + 4 a[2] + a[5]]}, {}] = , [4 a[2] + a[5]] For the domain, { a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, a[5] = 0, 2 <= a[6]} The value of the game = , [{f[1](0, a[2] - 1, 1, 0, 0, a[6])}, {}] = , [{[-1 + 4 a[2]]}, {}] = , [4 a[2]] For the domain, {a[1] = 0, a[2] = 0, 1 <= a[5], 1 <= a[3], 1 <= a[4], 2 <= a[6]} The value of the game = , [{ f[1](0, 0, a[3], a[4] - 1, a[5] + 1, a[6]), f[1](0, 0, a[3] - 1, a[4] + 1, a[5], a[6]), f[1](0, 0, a[3], a[4], a[5] - 1, a[6] + 1)}, {}] = , [{[-1 + 3 a[3] + 2 a[4] + a[5]]}, {}] = , [3 a[3] + 2 a[4] + a[5]] For the domain, { a[1] = 0, a[2] = 0, a[5] = 0, 1 <= a[3], 1 <= a[4], 2 <= a[6] } The value of the game = , [{ f[1](0, 0, a[3] - 1, a[4] + 1, 0, a[6]), f[1](0, 0, a[3], a[4] - 1, 1, a[6])}, {}] = , [{[-1 + 3 a[3] + 2 a[4]]}, {}] = , [3 a[3] + 2 a[4]] For the domain, { a[1] = 0, a[2] = 0, 1 <= a[5], a[4] = 0, 1 <= a[3], 2 <= a[6] } The value of the game = , [{ f[1](0, 0, a[3], 0, a[5] - 1, a[6] + 1), f[1](0, 0, a[3] - 1, 1, a[5], a[6])}, {}] = , [{[-1 + 3 a[3] + a[5]]}, {}] = , [3 a[3] + a[5]] For the domain, { a[1] = 0, a[2] = 0, a[4] = 0, a[5] = 0, 1 <= a[3], 2 <= a[6]} The value of the game = , [{f[1](0, 0, a[3] - 1, 1, 0, a[6])}, {}] = , [{[-1 + 3 a[3]]}, {}] = , [3 a[3]] For the domain, { a[1] = 0, a[3] = 0, a[2] = 0, 1 <= a[5], 1 <= a[4], 2 <= a[6] } The value of the game = , [{ f[1](0, 0, 0, a[4], a[5] - 1, a[6] + 1), f[1](0, 0, 0, a[4] - 1, a[5] + 1, a[6])}, {}] = , [{[-1 + 2 a[4] + a[5]]}, {}] = , [2 a[4] + a[5]] For the domain, { a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 0, 1 <= a[4], 2 <= a[6]} The value of the game = , [{f[1](0, 0, 0, a[4] - 1, 1, a[6])}, {}] = , [{[-1 + 2 a[4]]}, {}] = , [2 a[4]] For the domain, { a[1] = 0, a[3] = 0, a[2] = 0, 1 <= a[5], a[4] = 0, 2 <= a[6]} The value of the game = , [{f[1](0, 0, 0, 0, a[5] - 1, a[6] + 1)}, {}] = , [{[a[5] - 1]}, {}] = , [a[5]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0, a[5] = 0, 2 <= a[6]} The value of the game = , [{}, {}] = , [{}, {}] = , [0] ########## #, f[2], # ########## For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 0} The value of the game = , [{f[2](a[1] - 1, 1, 0, 0, 0)}, {f[3](a[1], 0, 0, 0) + [0]}] = , [{[{[4 a[1] - 4]}, {[4 a[1] - 4]}]}, {[4 a[1] - 3]}] = , [4 a[1] - 4] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0, a[5] = 0} The value of the game = , [{}, {f[3](0, 0, 0, 0) + [0]}] = , [{}, {[-3]}] = , [-4] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 0} 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[3](a[1], a[2], 0, 0) + [0]}] = , [{[4 a[1] + 3 a[2] - 3], [{[4 a[1] - 4 + 3 a[2]]}, {[4 a[1] - 4 + 3 a[2]]}]}, {[4 a[1] + 3 a[2] - 3]}] = , [{[4 a[1] + 3 a[2] - 3]}, {[4 a[1] + 3 a[2] - 3]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, a[5] = 0} The value of the game = , [{f[2](0, a[2] - 1, 1, 0, 0)}, {f[3](0, a[2], 0, 0) + [0]}] = , [{[-3 + 3 a[2]]}, {[-3 + 3 a[2]]}] For the domain, {1 <= a[2], a[3] = 1, 1 <= a[1], a[4] = 0, a[5] = 0} The value of the game = , [{f[2](a[1], a[2], 0, 1, 0), f[2](a[1], a[2] - 1, 2, 0, 0), f[2](a[1] - 1, a[2] + 1, 1, 0, 0)}, {f[3](a[1], a[2], 1, 0) + [0]}] = , [{[4 a[1] + 3 a[2] - 1]}, {[{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}]}] = , [4 a[1] + 3 a[2]] For the domain, {1 <= a[2], 2 <= a[3], 1 <= a[1], a[4] = 0, a[5] = 0} 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[2](a[1], a[2], a[3] - 1, 1, 0)}, {f[3](a[1], a[2], a[3], 0) + [0]}] = , [{[4 a[1] - 3 + 3 a[2] + 2 a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[4 a[1] + 3 a[2] + 2 a[3] - 2]} = , [4 a[1] + 3 a[2] + 2 a[3] - 2] For the domain, {a[2] = 0, a[3] = 1, 1 <= a[1], a[4] = 0, a[5] = 0} The value of the game = , [ {f[2](a[1], 0, 0, 1, 0), f[2](a[1] - 1, 1, 1, 0, 0)}, {f[3](a[1], 0, 1, 0) + [0]}] = , [{[4 a[1] - 1]}, {[{[4 a[1]]}, {[4 a[1]]}]}] = , [4 a[1]] For the domain, {a[2] = 0, 2 <= a[3], 1 <= a[1], a[4] = 0, a[5] = 0} The value of the game = , [{ f[2](a[1] - 1, 1, a[3], 0, 0), f[2](a[1], 0, a[3] - 1, 1, 0)} , {f[3](a[1], 0, a[3], 0) + [0]}] = , [{[4 a[1] - 3 + 2 a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[4 a[1] - 2 + 2 a[3]]} = , [4 a[1] - 2 + 2 a[3]] For the domain, {a[1] = 0, 1 <= a[2], a[3] = 1, a[4] = 0, a[5] = 0} The value of the game = , [ {f[2](0, a[2], 0, 1, 0), f[2](0, a[2] - 1, 2, 0, 0)}, {f[3](0, a[2], 1, 0) + [0]}] = , [{[-1 + 3 a[2]]}, {[{[3 a[2]]}, {[3 a[2]]}]}] = , [3 a[2]] For the domain, {a[1] = 0, 1 <= a[2], 2 <= a[3], a[4] = 0, a[5] = 0} The value of the game = , [{f[2](0, a[2], a[3] - 1, 1, 0), f[2](0, a[2] - 1, a[3] + 1, 0, 0)}, {f[3](0, a[2], a[3], 0) + [0]}] = , [{[-3 + 3 a[2] + 2 a[3]], [%1, %1]}, {[%1, %1]}] %1 := {[-2 + 3 a[2] + 2 a[3]]} = , [-2 + 3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 1, a[4] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, 0, 1, 0)}, {f[3](0, 0, 1, 0) + [0]}] = , [{[-1]}, {[{[0]}, {[0]}]}] = , [0] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[3], a[4] = 0, a[5] = 0} The value of the game = , [{f[2](0, 0, a[3] - 1, 1, 0)}, {f[3](0, 0, a[3], 0) + [0]}] = , [{[%1, %1]}, {[%1, %1]}] %1 := {[-2 + 2 a[3]]} = , [-2 + 2 a[3]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 1, a[5] = 0} The value of the game = , [{f[2](a[1], a[2] - 1, 1, 1, 0), f[2](a[1] - 1, a[2] + 1, 0, 1, 0), f[2](a[1], a[2], 0, 0, 1)} , {f[3](a[1], a[2], 0, 1) + [0]}] = , [{[4 a[1] + 3 a[2] - 2], [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}]}, {[4 a[1] + 3 a[2]]}] = , [4 a[1] + 3 a[2] - 1] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 1, a[5] = 0} 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]}] = , [{[4 a[1] - 2]}, {[4 a[1]]}] = , [4 a[1] - 1] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 1, a[5] = 0} The value of the game = , [ {f[2](0, a[2], 0, 0, 1), f[2](0, a[2] - 1, 1, 1, 0)}, {f[3](0, a[2], 0, 1) + [0]}] = , [{[{[-1 + 3 a[2]]}, {[-1 + 3 a[2]]}]}, {[3 a[2]]}] = , [-1 + 3 a[2]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 1, a[5] = 0} The value of the game = , [{f[2](0, 0, 0, 0, 1)}, {f[3](0, 0, 0, 1) + [0]}] = , [{[-2]}, {[0]}] = , [-1] For the domain, {1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 0, 1 <= a[3]} The value of the game = , [{ f[2](a[1] - 1, a[2] + 1, a[3], a[4], 0), f[2](a[1], a[2], a[3] - 1, a[4] + 1, 0), f[2](a[1], a[2] - 1, a[3] + 1, a[4], 0), f[2](a[1], a[2], a[3], a[4] - 1, 1)}, {f[3](a[1], a[2], a[3], a[4]) + [0]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1], [ {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 2]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}] For the domain, {a[3] = 0, 1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 0} The value of the game = , [{f[2](a[1], a[2], 0, a[4] - 1, 1), f[2](a[1], a[2] - 1, 1, a[4], 0), f[2](a[1] - 1, a[2] + 1, 0, a[4], 0)}, {f[3](a[1], a[2], 0, a[4]) + [0]}] = , [{[4 a[1] + 3 a[2] - 1 + a[4]], [ {[4 a[1] + 3 a[2] - 2 + a[4]]}, {[4 a[1] + 3 a[2] - 2 + a[4]]}]}, {[4 a[1] + 3 a[2] - 1 + a[4]]}] = , [{[4 a[1] + 3 a[2] - 1 + a[4]]}, {[4 a[1] + 3 a[2] - 1 + a[4]]}] For the domain, {a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 0, 1 <= a[3]} The value of the game = , [{f[2](a[1], 0, a[3], a[4] - 1, 1), f[2](a[1], 0, a[3] - 1, a[4] + 1, 0), f[2](a[1] - 1, 1, a[3], a[4], 0)}, {f[3](a[1], 0, a[3], a[4]) + [0]}] = , [{[4 a[1] - 1 + 2 a[3] + a[4]], [ {[4 a[1] - 2 + 2 a[3] + a[4]]}, {[4 a[1] - 2 + 2 a[3] + a[4]]}]}, {[4 a[1] - 1 + 2 a[3] + a[4]]}] = , [{[4 a[1] - 1 + 2 a[3] + a[4]]}, {[4 a[1] - 1 + 2 a[3] + a[4]]}] For the domain, {a[3] = 0, a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 0} The value of the game = , [{ f[2](a[1] - 1, 1, 0, a[4], 0), f[2](a[1], 0, 0, a[4] - 1, 1)} , {f[3](a[1], 0, 0, a[4]) + [0]}] = , [{[4 a[1] - 1 + a[4]], [{[4 a[1] - 2 + a[4]]}, {[4 a[1] - 2 + a[4]]}]}, {[4 a[1] - 1 + a[4]]}] = , [{[4 a[1] - 1 + a[4]]}, {[4 a[1] - 1 + a[4]]}] For the domain, {a[1] = 0, 1 <= a[2], 2 <= a[4], a[5] = 0, 1 <= a[3]} The value of the game = , [{f[2](0, a[2], a[3], a[4] - 1, 1), f[2](0, a[2] - 1, a[3] + 1, a[4], 0), f[2](0, a[2], a[3] - 1, a[4] + 1, 0)}, {f[3](0, a[2], a[3], a[4]) + [0]}] = , [{[{[-2 + 3 a[2] + 2 a[3] + a[4]]}, {[-2 + 3 a[2] + 2 a[3] + a[4]]}], [-1 + 3 a[2] + 2 a[3] + a[4]]}, {[-1 + 3 a[2] + 2 a[3] + a[4]]}] = , [{[-1 + 3 a[2] + 2 a[3] + a[4]]}, {[-1 + 3 a[2] + 2 a[3] + a[4]]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[4], a[5] = 0} The value of the game = , [{ f[2](0, a[2] - 1, 1, a[4], 0), f[2](0, a[2], 0, a[4] - 1, 1)} , {f[3](0, a[2], 0, a[4]) + [0]}] = , [{[{[-2 + 3 a[2] + a[4]]}, {[-2 + 3 a[2] + a[4]]}], [-1 + 3 a[2] + a[4]]}, {[-1 + 3 a[2] + a[4]]}] = , [{[-1 + 3 a[2] + a[4]]}, {[-1 + 3 a[2] + a[4]]}] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[4], a[5] = 0, 1 <= a[3]} The value of the game = , [{f[2](0, 0, a[3] - 1, a[4] + 1, 0), f[2](0, 0, a[3], a[4] - 1, 1)}, {f[3](0, 0, a[3], a[4]) + [0]}] = , [{[{[-2 + 2 a[3] + a[4]]}, {[-2 + 2 a[3] + a[4]]}], [-1 + 2 a[3] + a[4]]}, {[-1 + 2 a[3] + a[4]]}] = , [{[-1 + 2 a[3] + a[4]]}, {[-1 + 2 a[3] + a[4]]}] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 2 <= a[4], a[5] = 0} The value of the game = , [{f[2](0, 0, 0, a[4] - 1, 1)}, {f[3](0, 0, 0, a[4]) + [0]}] = , [{[a[4] - 1]}, {[a[4] - 1]}] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 1, a[5] = 0, 1 <= a[3]} The value of the game = , [{f[2](a[1] - 1, a[2] + 1, a[3], 1, 0), f[2](a[1], a[2], a[3] - 1, 2, 0), f[2](a[1], a[2] - 1, a[3] + 1, 1, 0), f[2](a[1], a[2], a[3], 0, 1)}, {f[3](a[1], a[2], a[3], 1) + [0]}] = , [{[4 a[1] + 3 a[2] + 2 a[3]], [ {[4 a[1] + 3 a[2] + 2 a[3] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] - 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}] = , [{[4 a[1] + 3 a[2] + 2 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}] For the domain, {a[2] = 0, 1 <= a[1], a[4] = 1, a[5] = 0, 1 <= a[3]} The value of the game = , [{f[2](a[1], 0, a[3], 0, 1), f[2](a[1], 0, a[3] - 1, 2, 0), f[2](a[1] - 1, 1, a[3], 1, 0)} , {f[3](a[1], 0, a[3], 1) + [0]}] = , [{[{[4 a[1] - 1 + 2 a[3]]}, {[4 a[1] - 1 + 2 a[3]]}], [4 a[1] + 2 a[3]]}, {[4 a[1] + 2 a[3]]}] = , [{[4 a[1] + 2 a[3]]}, {[4 a[1] + 2 a[3]]}] For the domain, {a[1] = 0, 1 <= a[2], a[4] = 1, a[5] = 0, 1 <= a[3]} The value of the game = , [{f[2](0, a[2], a[3] - 1, 2, 0), f[2](0, a[2], a[3], 0, 1), f[2](0, a[2] - 1, a[3] + 1, 1, 0)} , {f[3](0, a[2], a[3], 1) + [0]}] = , [{[3 a[2] + 2 a[3]], [{[-1 + 3 a[2] + 2 a[3]]}, {[-1 + 3 a[2] + 2 a[3]]}]}, {[3 a[2] + 2 a[3]]}] = , [{[3 a[2] + 2 a[3]]}, {[3 a[2] + 2 a[3]]}] For the domain, {a[1] = 0, a[2] = 0, a[4] = 1, a[5] = 0, 1 <= a[3]} The value of the game = , [ {f[2](0, 0, a[3], 0, 1), f[2](0, 0, a[3] - 1, 2, 0)}, {f[3](0, 0, a[3], 1) + [0]}] = , [{[2 a[3]], [{[-1 + 2 a[3]]}, {[-1 + 2 a[3]]}]}, {[2 a[3]]}] = , [{[2 a[3]]}, {[2 a[3]]}] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 0} The value of the game = , [ {f[1](a[1], 0, 0, 0, 0, 0) + [0], f[2](a[1] - 1, 1, 0, 0, 1)} , {f[3](a[1], 0, 0, 0) + [2]}] = , [{[{[4 a[1] - 2]}, {[4 a[1] - 2]}], [{[4 a[1] - 4]}, {[4 a[1] - 4]}]}, {[4 a[1] - 1]}] = , [4 a[1] - 2] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 1, a[4] = 0} The value of the game = , [{f[1](0, 0, 0, 0, 0, 0) + [0]}, {f[3](0, 0, 0, 0) + [2]}] = , [{[-5]}, {[-1]}] = , [-2] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 0} The value of the game = , [{f[1](a[1], a[2], 0, 0, 0, 0) + [0], 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) + [2]}] = , [{[{[4 a[1] + 3 a[2] - 2]}, {[4 a[1] + 3 a[2] - 2]}], [4 a[1] + 3 a[2] - 3], [4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}] = , [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 1, a[4] = 0} The value of the game = , [ {f[1](0, a[2], 0, 0, 0, 0) + [0], f[2](0, a[2] - 1, 1, 0, 1)} , {f[3](0, a[2], 0, 0) + [2]}] = , [{[-3 + 3 a[2]], [-1 + 3 a[2]]}, {[-1 + 3 a[2]]}] = , [{[-1 + 3 a[2]]}, {[-1 + 3 a[2]]}] For the domain, {1 <= a[2], a[3] = 1, 1 <= a[1], a[5] = 1, a[4] = 0} The value of the game = , [{f[2](a[1], a[2], 0, 1, 1), f[1](a[1], a[2], 1, 0, 0, 0) + [0], f[2](a[1], a[2] - 1, 2, 0, 1), f[2](a[1] - 1, a[2] + 1, 1, 0, 1)}, {f[3](a[1], a[2], 1, 0) + [2]}] = , [{[4 a[1] + 3 a[2] + 1], [4 a[1] + 3 a[2] - 1]}, {[{[4 a[1] + 3 a[2] + 2]}, {[4 a[1] + 3 a[2] + 2]}]}] = , [4 a[1] + 3 a[2] + 2] For the domain, {1 <= a[2], 2 <= a[3], 1 <= a[1], a[5] = 1, a[4] = 0} The value of the game = , [{f[1](a[1], a[2], a[3], 0, 0, 0) + [0], f[2](a[1] - 1, a[2] + 1, a[3], 0, 1), f[2](a[1], a[2], a[3] - 1, 1, 1), f[2](a[1], a[2] - 1, a[3] + 1, 0, 1)}, {f[3](a[1], a[2], a[3], 0) + [2]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 1], [ {[4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}]}, { [{[4 a[1] + 3 a[2] + 2 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3]]}]} ] = , [4 a[1] + 3 a[2] + 2 a[3]] For the domain, {a[2] = 0, a[3] = 1, 1 <= a[1], a[5] = 1, a[4] = 0} The value of the game = , [{f[2](a[1], 0, 0, 1, 1), f[1](a[1], 0, 1, 0, 0, 0) + [0], f[2](a[1] - 1, 1, 1, 0, 1)}, {f[3](a[1], 0, 1, 0) + [2]}] = , [{[4 a[1] - 1], [4 a[1] + 1]}, {[{[4 a[1] + 2]}, {[4 a[1] + 2]}]}] = , [4 a[1] + 2] For the domain, {a[2] = 0, 2 <= a[3], 1 <= a[1], a[5] = 1, a[4] = 0} The value of the game = , [{f[1](a[1], 0, a[3], 0, 0, 0) + [0], f[2](a[1], 0, a[3] - 1, 1, 1), f[2](a[1] - 1, 1, a[3], 0, 1)} , {f[3](a[1], 0, a[3], 0) + [2]}] = , [{[{[4 a[1] - 2 + 2 a[3]]}, {[4 a[1] - 2 + 2 a[3]]}], [4 a[1] - 1 + 2 a[3]]}, {[{[4 a[1] + 2 a[3]]}, {[4 a[1] + 2 a[3]]}]}] = , [4 a[1] + 2 a[3]] For the domain, {a[1] = 0, 1 <= a[2], a[3] = 1, a[5] = 1, a[4] = 0} The value of the game = , [{f[2](0, a[2], 0, 1, 1), f[1](0, a[2], 1, 0, 0, 0) + [0], f[2](0, a[2] - 1, 2, 0, 1)}, {f[3](0, a[2], 1, 0) + [2]}] = , [{[1 + 3 a[2]], [-1 + 3 a[2]]}, {[{[3 a[2] + 2]}, {[3 a[2] + 2]}]}] = , [3 a[2] + 2] For the domain, {a[1] = 0, 1 <= a[2], 2 <= a[3], a[5] = 1, a[4] = 0} The value of the game = , [{f[1](0, a[2], a[3], 0, 0, 0) + [0], f[2](0, a[2] - 1, a[3] + 1, 0, 1), f[2](0, a[2], a[3] - 1, 1, 1)}, {f[3](0, a[2], a[3], 0) + [2]}] = , [{[{[-2 + 3 a[2] + 2 a[3]]}, {[-2 + 3 a[2] + 2 a[3]]}], [-1 + 3 a[2] + 2 a[3]]}, {[{[3 a[2] + 2 a[3]]}, {[3 a[2] + 2 a[3]]}]}] = , [3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 1, a[5] = 1, a[4] = 0} The value of the game = , [ {f[2](0, 0, 0, 1, 1), f[1](0, 0, 1, 0, 0, 0) + [0]}, {f[3](0, 0, 1, 0) + [2]}] = , [{[-1], [1]}, {[{[2]}, {[2]}]}] = , [2] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[3], a[5] = 1, a[4] = 0} The value of the game = , [ {f[1](0, 0, a[3], 0, 0, 0) + [0], f[2](0, 0, a[3] - 1, 1, 1)} , {f[3](0, 0, a[3], 0) + [2]}] = , [{[{[-2 + 2 a[3]]}, {[-2 + 2 a[3]]}], [-1 + 2 a[3]]}, {[{[2 a[3]]}, {[2 a[3]]}]}] = , [2 a[3]] For the domain, {1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 1, 1 <= a[3]} The value of the game = , [{f[2](a[1], a[2], a[3], 0, 2), f[1](a[1], a[2], a[3], 1, 0, 0) + [0], f[2](a[1], a[2], a[3] - 1, 2, 1), f[2](a[1] - 1, a[2] + 1, a[3], 1, 1), f[2](a[1], a[2] - 1, a[3] + 1, 1, 1)}, {f[3](a[1], a[2], a[3], 1) + [2]}] = , [{[4 a[1] + 3 a[2] + 2 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 2]}] = , [4 a[1] + 3 a[2] + 2 a[3] + 1] For the domain, {1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 1, 1 <= a[3]} The value of the game = , [{ f[1](a[1], a[2], a[3], a[4], 0, 0) + [0], f[2](a[1], a[2] - 1, a[3] + 1, a[4], 1), 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], a[3] - 1, a[4] + 1, 1)}, {f[3](a[1], a[2], a[3], a[4]) + [2]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}] = , [4 a[1] + 3 a[2] + 2 a[3] + a[4]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[5] = 1, a[4] = 1} The value of the game = , [{f[1](a[1], a[2], 0, 1, 0, 0) + [0], f[2](a[1], a[2], 0, 0, 2), f[2](a[1], a[2] - 1, 1, 1, 1), f[2](a[1] - 1, a[2] + 1, 0, 1, 1)}, {f[3](a[1], a[2], 0, 1) + [2]}] = , [{[4 a[1] + 3 a[2]], [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] - 1]}]}, {[4 a[1] + 3 a[2] + 2]}] = , [4 a[1] + 3 a[2] + 1] For the domain, {a[3] = 0, 1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 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[1](a[1], a[2], 0, a[4], 0, 0) + [0]}, {f[3](a[1], a[2], 0, a[4]) + [2]}] = , [{[4 a[1] + 3 a[2] - 1 + a[4]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}] = , [4 a[1] + 3 a[2] + a[4]] For the domain, {a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 1, 1 <= a[3]} The value of the game = , [{f[2](a[1], 0, a[3], 0, 2), f[1](a[1], 0, a[3], 1, 0, 0) + [0], f[2](a[1] - 1, 1, a[3], 1, 1), f[2](a[1], 0, a[3] - 1, 2, 1)} , {f[3](a[1], 0, a[3], 1) + [2]}] = , [{[4 a[1] + 2 a[3]]}, {[4 a[1] + 2 + 2 a[3]]}] = , [4 a[1] + 2 a[3] + 1] For the domain, {a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 1, 1 <= a[3]} The value of the game = , [{f[1](a[1], 0, a[3], a[4], 0, 0) + [0], f[2](a[1], 0, a[3] - 1, a[4] + 1, 1), f[2](a[1], 0, a[3], a[4] - 1, 2), f[2](a[1] - 1, 1, a[3], a[4], 1)}, {f[3](a[1], 0, a[3], a[4]) + [2]}] = , [{[4 a[1] - 1 + 2 a[3] + a[4]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}] = , [4 a[1] + 2 a[3] + a[4]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[5] = 1, a[4] = 1} The value of the game = , [{f[2](a[1], 0, 0, 0, 2), f[1](a[1], 0, 0, 1, 0, 0) + [0], f[2](a[1] - 1, 1, 0, 1, 1)}, {f[3](a[1], 0, 0, 1) + [2]}] = , [{[4 a[1]], [4 a[1] - 2]}, {[4 a[1] + 2]}] = , [4 a[1] + 1] For the domain, {a[3] = 0, a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 1} The value of the game = , [{f[1](a[1], 0, 0, a[4], 0, 0) + [0], f[2](a[1], 0, 0, a[4] - 1, 2), f[2](a[1] - 1, 1, 0, a[4], 1)} , {f[3](a[1], 0, 0, a[4]) + [2]}] = , [{[4 a[1] - 1 + a[4]]}, {[4 a[1] + 1 + a[4]]}] = , [4 a[1] + a[4]] For the domain, {a[1] = 0, 1 <= a[2], a[5] = 1, a[4] = 1, 1 <= a[3]} The value of the game = , [{f[2](0, a[2], a[3], 0, 2), f[1](0, a[2], a[3], 1, 0, 0) + [0], f[2](0, a[2] - 1, a[3] + 1, 1, 1), f[2](0, a[2], a[3] - 1, 2, 1)}, {f[3](0, a[2], a[3], 1) + [2]}] = , [{[3 a[2] + 2 a[3]]}, {[2 + 3 a[2] + 2 a[3]]}] = , [3 a[2] + 2 a[3] + 1] For the domain, {a[1] = 0, 1 <= a[2], 2 <= a[4], a[5] = 1, 1 <= a[3]} The value of the game = , [{f[1](0, a[2], a[3], a[4], 0, 0) + [0], f[2](0, a[2], a[3] - 1, a[4] + 1, 1), f[2](0, a[2], a[3], a[4] - 1, 2), f[2](0, a[2] - 1, a[3] + 1, a[4], 1)}, {f[3](0, a[2], a[3], a[4]) + [2]}] = , [{[-1 + 3 a[2] + 2 a[3] + a[4]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] = , [3 a[2] + 2 a[3] + a[4]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[5] = 1, a[4] = 1} The value of the game = , [{f[2](0, a[2], 0, 0, 2), f[1](0, a[2], 0, 1, 0, 0) + [0], f[2](0, a[2] - 1, 1, 1, 1)}, {f[3](0, a[2], 0, 1) + [2]}] = , [{[{[-1 + 3 a[2]]}, {[-1 + 3 a[2]]}], [3 a[2]]}, {[2 + 3 a[2]]}] = , [3 a[2] + 1] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[4], a[5] = 1} The value of the game = , [{f[1](0, a[2], 0, a[4], 0, 0) + [0], 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]) + [2]}] = , [{[-1 + 3 a[2] + a[4]]}, {[1 + 3 a[2] + a[4]]}] = , [3 a[2] + a[4]] For the domain, {a[1] = 0, a[2] = 0, a[5] = 1, a[4] = 1, 1 <= a[3]} The value of the game = , [{f[2](0, 0, a[3], 0, 2), f[1](0, 0, a[3], 1, 0, 0) + [0], f[2](0, 0, a[3] - 1, 2, 1)}, {f[3](0, 0, a[3], 1) + [2]}] = , [{[2 a[3]]}, {[2 + 2 a[3]]}] = , [2 a[3] + 1] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[4], a[5] = 1, 1 <= a[3]} The value of the game = , [{f[1](0, 0, a[3], a[4], 0, 0) + [0], f[2](0, 0, a[3], a[4] - 1, 2), f[2](0, 0, a[3] - 1, a[4] + 1, 1)}, {f[3](0, 0, a[3], a[4]) + [2]}] = , [{[-1 + 2 a[3] + a[4]]}, {[1 + 2 a[3] + a[4]]}] = , [2 a[3] + a[4]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[5] = 1, a[4] = 1} The value of the game = , [ {f[2](0, 0, 0, 0, 2), f[1](0, 0, 0, 1, 0, 0) + [0]}, {f[3](0, 0, 0, 1) + [2]}] = , [{[-2], [0]}, {[2]}] = , [1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 2 <= a[4], a[5] = 1} The value of the game = , [ {f[1](0, 0, 0, a[4], 0, 0) + [0], f[2](0, 0, 0, a[4] - 1, 2)} , {f[3](0, 0, 0, a[4]) + [2]}] = , [{[a[4] - 1]}, {[a[4] + 1]}] = , [a[4]] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 1, 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](a[1], a[2], a[3], 1, 1, 0) + [0], f[2](a[1], a[2], a[3] - 1, 2, 2), f[2](a[1], a[2], a[3], 0, 3), f[2](a[1], a[2] - 1, a[3] + 1, 1, 2), f[2](a[1] - 1, a[2] + 1, a[3], 1, 2)}, {}] = , [{[{[4 a[1] + 3 a[2] + 2 a[3] + 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}], [4 a[1] + 3 a[2] + 2 a[3]] }, {}] = , [4 a[1] + 3 a[2] + 2 a[3] + 1] For the domain, {1 <= a[2], 2 <= a[4], 1 <= a[1], 1 <= a[3], a[5] = 2} The value of the game = , [{ f[1](a[1], a[2], a[3], a[4], 1, 0) + [0], f[2](a[1], a[2], a[3] - 1, a[4] + 1, 2), f[2](a[1], a[2], a[3], a[4] - 1, 3), f[2](a[1] - 1, a[2] + 1, a[3], a[4], 2), f[2](a[1], a[2] - 1, a[3] + 1, a[4], 2)}, {}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1], [ {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}]}, {}] = , [4 a[1] + 3 a[2] + 2 a[3] + a[4]] For the domain, {1 <= a[2], 1 <= a[1], 1 <= a[3], 1 <= a[4], a[5] = 3} The value of the game = , [{ f[1](a[1], a[2], a[3], a[4], 2, 0) + [0], f[2](a[1], a[2], a[3], a[4] - 1, 4), f[2](a[1] - 1, a[2] + 1, a[3], a[4], 3), f[2](a[1], a[2] - 1, a[3] + 1, a[4], 3), f[2](a[1], a[2], a[3] - 1, a[4] + 1, 3)}, {}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1], [{[ {[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}]}, {}] = , [4 a[1] + 3 a[2] + 2 a[3] + a[4]] For the domain, {1 <= a[2], 1 <= a[1], 4 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[1](a[1], a[2], a[3], a[4], a[5] - 1, 0) + [0], f[2](a[1], a[2] - 1, a[3] + 1, a[4], a[5]), f[2](a[1] - 1, a[2] + 1, a[3], a[4], a[5]), f[2](a[1], a[2], a[3], a[4] - 1, a[5] + 1), f[2](a[1], a[2], a[3] - 1, a[4] + 1, a[5])}, {}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1], [{[ {[5 a[1] + 4 a[2] + 3 a[3] + 2 a[4] + a[5] - 3]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4]]}]}, {}] = , [4 a[1] + 3 a[2] + 2 a[3] + a[4]] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 0, 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](a[1], a[2], a[3], 0, 1, 0) + [0], f[2](a[1], a[2], a[3] - 1, 1, 2), f[2](a[1], a[2] - 1, a[3] + 1, 0, 2), f[2](a[1] - 1, a[2] + 1, a[3], 0, 2)}, {}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 1]}, {}] = , [4 a[1] + 3 a[2] + 2 a[3]] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 0, 1 <= a[3], a[5] = 3} The value of the game = , [{f[1](a[1], a[2], a[3], 0, 2, 0) + [0], f[2](a[1], a[2] - 1, a[3] + 1, 0, 3), f[2](a[1] - 1, a[2] + 1, a[3], 0, 3), f[2](a[1], a[2], a[3] - 1, 1, 3)}, {}] = , [{[{[{[5 a[1] + 4 a[2] + 3 a[3]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}], [4 a[1] + 3 a[2] + 2 a[3] - 1] }, {}] = , [4 a[1] + 3 a[2] + 2 a[3]] For the domain, {1 <= a[2], 1 <= a[1], 4 <= a[5], a[4] = 0, 1 <= a[3]} The value of the game = , [{ f[1](a[1], a[2], a[3], 0, a[5] - 1, 0) + [0], f[2](a[1], a[2], a[3] - 1, 1, a[5]), 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])}, {}] = , [{[{[{[5 a[1] + 4 a[2] + 3 a[3] - 3 + a[5]]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {[4 a[1] + 3 a[2] + 2 a[3]]}], [4 a[1] + 3 a[2] + 2 a[3] - 1] }, {}] = , [4 a[1] + 3 a[2] + 2 a[3]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 1, a[5] = 2} The value of the game = , [{f[1](a[1], a[2], 0, 1, 1, 0) + [0], f[2](a[1] - 1, a[2] + 1, 0, 1, 2), f[2](a[1], a[2] - 1, 1, 1, 2), f[2](a[1], a[2], 0, 0, 3)}, {} ] = , [{[4 a[1] + 3 a[2]]}, {}] = , [4 a[1] + 3 a[2] + 1] For the domain, {a[3] = 0, 1 <= a[2], 2 <= a[4], 1 <= a[1], a[5] = 2} The value of the game = , [{f[1](a[1], a[2], 0, a[4], 1, 0) + [0], f[2](a[1], a[2] - 1, 1, a[4], 2), f[2](a[1] - 1, a[2] + 1, 0, a[4], 2), f[2](a[1], a[2], 0, a[4] - 1, 3)}, {}] = , [{[{[4 a[1] + 3 a[2] + a[4]]}, {[4 a[1] + 3 a[2] + a[4]]}], [4 a[1] + 3 a[2] - 1 + a[4]]}, {}] = , [4 a[1] + 3 a[2] + a[4]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], 1 <= a[4], a[5] = 3} The value of the game = , [{f[1](a[1], a[2], 0, a[4], 2, 0) + [0], f[2](a[1], a[2], 0, a[4] - 1, 4), f[2](a[1], a[2] - 1, 1, a[4], 3), f[2](a[1] - 1, a[2] + 1, 0, a[4], 3)}, {}] = , [{[4 a[1] + 3 a[2] - 1 + a[4]], [{[ {[5 a[1] + 4 a[2] + 2 a[4]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}] }, {[4 a[1] + 3 a[2] + a[4]]}]}, {}] = , [4 a[1] + 3 a[2] + a[4]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], 4 <= a[5], 1 <= a[4]} The value of the game = , [{ f[1](a[1], a[2], 0, a[4], a[5] - 1, 0) + [0], f[2](a[1], a[2], 0, a[4] - 1, a[5] + 1), 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])}, {}] = , [{[4 a[1] + 3 a[2] - 1 + a[4]], [{[ {[5 a[1] + 4 a[2] - 3 + 2 a[4] + a[5]]}, {[4 a[1] + 3 a[2] + 1 + a[4]]}]}, {[4 a[1] + 3 a[2] + a[4]]}] }, {}] = , [4 a[1] + 3 a[2] + a[4]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 2} The value of the game = , [{f[1](a[1], a[2], 0, 0, 1, 0) + [0], f[2](a[1] - 1, a[2] + 1, 0, 0, 2), f[2](a[1], a[2] - 1, 1, 0, 2)}, {}] = , [{[4 a[1] + 3 a[2] - 1]}, {}] = , [4 a[1] + 3 a[2]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0, a[5] = 3} The value of the game = , [{f[1](a[1], a[2], 0, 0, 2, 0) + [0], f[2](a[1] - 1, a[2] + 1, 0, 0, 3), f[2](a[1], a[2] - 1, 1, 0, 3)}, {}] = , [{[{[4 a[1] + 3 a[2]]}, {[4 a[1] + 3 a[2]]}], [4 a[1] + 3 a[2] - 1]}, {}] = , [4 a[1] + 3 a[2]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], 4 <= a[5], a[4] = 0} The value of the game = , [{ f[1](a[1], a[2], 0, 0, a[5] - 1, 0) + [0], f[2](a[1], a[2] - 1, 1, 0, a[5]), f[2](a[1] - 1, a[2] + 1, 0, 0, a[5])}, {}] = , [{[ {[{[5 a[1] + 4 a[2] - 3 + a[5]]}, {[4 a[1] + 3 a[2] + 1]}]}, {[4 a[1] + 3 a[2]]}], [4 a[1] + 3 a[2] - 1]}, {}] = , [4 a[1] + 3 a[2]] For the domain, {a[2] = 0, 1 <= a[1], a[4] = 1, 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](a[1], 0, a[3], 1, 1, 0) + [0], f[2](a[1], 0, a[3] - 1, 2, 2), f[2](a[1] - 1, 1, a[3], 1, 2), f[2](a[1], 0, a[3], 0, 3)}, {}] = , [{[{[4 a[1] + 2 a[3] + 1]}, {[4 a[1] + 2 a[3] + 1]}], [4 a[1] + 2 a[3]]}, {}] = , [4 a[1] + 2 a[3] + 1] For the domain, {a[2] = 0, 2 <= a[4], 1 <= a[1], 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](a[1], 0, a[3], a[4], 1, 0) + [0], f[2](a[1], 0, a[3] - 1, a[4] + 1, 2), f[2](a[1] - 1, 1, a[3], a[4], 2), f[2](a[1], 0, a[3], a[4] - 1, 3)}, {}] = , [{[4 a[1] - 1 + 2 a[3] + a[4]], [{[4 a[1] + 2 a[3] + a[4]]}, {[4 a[1] + 2 a[3] + a[4]]}]}, {} ] = , [4 a[1] + 2 a[3] + a[4]] For the domain, {a[2] = 0, 1 <= a[1], 1 <= a[3], 1 <= a[4], a[5] = 3} The value of the game = , [{f[1](a[1], 0, a[3], a[4], 2, 0) + [0], f[2](a[1] - 1, 1, a[3], a[4], 3), f[2](a[1], 0, a[3], a[4] - 1, 4), f[2](a[1], 0, a[3] - 1, a[4] + 1, 3)}, {}] = , [{[4 a[1] - 1 + 2 a[3] + a[4]], [{[ {[5 a[1] + 3 a[3] + 2 a[4]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}] }, {[4 a[1] + 2 a[3] + a[4]]}]}, {}] = , [4 a[1] + 2 a[3] + a[4]] For the domain, {a[2] = 0, 1 <= a[1], 4 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[1](a[1], 0, a[3], a[4], a[5] - 1, 0) + [0], f[2](a[1], 0, a[3] - 1, a[4] + 1, a[5]), f[2](a[1], 0, a[3], a[4] - 1, a[5] + 1), f[2](a[1] - 1, 1, a[3], a[4], a[5])}, {}] = , [{[4 a[1] - 1 + 2 a[3] + a[4]], [{[ {[5 a[1] - 3 + 3 a[3] + 2 a[4] + a[5]]}, {[4 a[1] + 1 + 2 a[3] + a[4]]}]}, {[4 a[1] + 2 a[3] + a[4]]}] }, {}] = , [4 a[1] + 2 a[3] + a[4]] For the domain, {a[2] = 0, 1 <= a[1], a[4] = 0, 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](a[1], 0, a[3], 0, 1, 0) + [0], f[2](a[1], 0, a[3] - 1, 1, 2), f[2](a[1] - 1, 1, a[3], 0, 2)} , {}] = , [{[4 a[1] - 1 + 2 a[3]]}, {}] = , [4 a[1] + 2 a[3]] For the domain, {a[2] = 0, 1 <= a[1], a[4] = 0, 1 <= a[3], a[5] = 3} The value of the game = , [{f[1](a[1], 0, a[3], 0, 2, 0) + [0], f[2](a[1], 0, a[3] - 1, 1, 3), f[2](a[1] - 1, 1, a[3], 0, 3)} , {}] = , [{[4 a[1] - 1 + 2 a[3]], [ {[{[5 a[1] + 3 a[3]]}, {[4 a[1] + 2 a[3] + 1]}]}, {[4 a[1] + 2 a[3]]}]}, {}] = , [4 a[1] + 2 a[3]] For the domain, {a[2] = 0, 1 <= a[1], 4 <= a[5], a[4] = 0, 1 <= a[3]} The value of the game = , [{ f[1](a[1], 0, a[3], 0, a[5] - 1, 0) + [0], f[2](a[1] - 1, 1, a[3], 0, a[5]), f[2](a[1], 0, a[3] - 1, 1, a[5])}, {}] = , [{[4 a[1] - 1 + 2 a[3]], [ {[{[5 a[1] - 3 + 3 a[3] + a[5]]}, {[4 a[1] + 2 a[3] + 1]}]}, {[4 a[1] + 2 a[3]]}]}, {}] = , [4 a[1] + 2 a[3]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 1, a[5] = 2} The value of the game = , [{f[1](a[1], 0, 0, 1, 1, 0) + [0], f[2](a[1] - 1, 1, 0, 1, 2), f[2](a[1], 0, 0, 0, 3)}, {}] = , [{[4 a[1]]}, {}] = , [4 a[1] + 1] For the domain, {a[3] = 0, a[2] = 0, 2 <= a[4], 1 <= a[1], a[5] = 2} The value of the game = , [{f[1](a[1], 0, 0, a[4], 1, 0) + [0], f[2](a[1], 0, 0, a[4] - 1, 3), f[2](a[1] - 1, 1, 0, a[4], 2)} , {}] = , [{[4 a[1] - 1 + a[4]], [{[4 a[1] + a[4]]}, {[4 a[1] + a[4]]}]} , {}] = , [4 a[1] + a[4]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], 1 <= a[4], a[5] = 3} The value of the game = , [{f[1](a[1], 0, 0, a[4], 2, 0) + [0], f[2](a[1], 0, 0, a[4] - 1, 4), f[2](a[1] - 1, 1, 0, a[4], 3)} , {}] = , [{[4 a[1] - 1 + a[4]], [ {[{[5 a[1] + 2 a[4]]}, {[4 a[1] + 1 + a[4]]}]}, {[4 a[1] + a[4]]}]}, {}] = , [4 a[1] + a[4]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], 4 <= a[5], 1 <= a[4]} The value of the game = , [{ f[1](a[1], 0, 0, a[4], a[5] - 1, 0) + [0], f[2](a[1], 0, 0, a[4] - 1, a[5] + 1), f[2](a[1] - 1, 1, 0, a[4], a[5])}, {}] = , [{[4 a[1] - 1 + a[4]], [ {[{[5 a[1] - 3 + 2 a[4] + a[5]]}, {[4 a[1] + 1 + a[4]]}]}, {[4 a[1] + a[4]]}]}, {}] = , [4 a[1] + a[4]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 2} The value of the game = , [ {f[1](a[1], 0, 0, 0, 1, 0) + [0], f[2](a[1] - 1, 1, 0, 0, 2)} , {}] = , [{[4 a[1] - 1], [{[4 a[1] - 2]}, {[4 a[1] - 2]}]}, {}] = , [4 a[1]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0, a[5] = 3} The value of the game = , [ {f[1](a[1], 0, 0, 0, 2, 0) + [0], f[2](a[1] - 1, 1, 0, 0, 3)} , {}] = , [{[4 a[1] - 1]}, {}] = , [4 a[1]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], 4 <= a[5], a[4] = 0} The value of the game = , [{f[1](a[1], 0, 0, 0, a[5] - 1, 0) + [0], f[2](a[1] - 1, 1, 0, 0, a[5])}, {}] = , [{[4 a[1] - 1], [{[{[5 a[1] - 3 + a[5]]}, {[4 a[1] + 1]}]}, {[4 a[1]]}]}, {}] = , [4 a[1]] For the domain, {a[1] = 0, 1 <= a[2], a[4] = 1, 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](0, a[2], a[3], 1, 1, 0) + [0], f[2](0, a[2], a[3] - 1, 2, 2), f[2](0, a[2] - 1, a[3] + 1, 1, 2), f[2](0, a[2], a[3], 0, 3)} , {}] = , [{[3 a[2] + 2 a[3]], [{[3 a[2] + 2 a[3] + 1]}, {[3 a[2] + 2 a[3] + 1]}]}, {}] = , [3 a[2] + 2 a[3] + 1] For the domain, {a[1] = 0, 1 <= a[2], 2 <= a[4], 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](0, a[2], a[3], a[4], 1, 0) + [0], f[2](0, a[2] - 1, a[3] + 1, a[4], 2), f[2](0, a[2], a[3], a[4] - 1, 3), f[2](0, a[2], a[3] - 1, a[4] + 1, 2)}, {}] = , [{[{[3 a[2] + 2 a[3] + a[4]]}, {[3 a[2] + 2 a[3] + a[4]]}], [-1 + 3 a[2] + 2 a[3] + a[4]]}, {}] = , [3 a[2] + 2 a[3] + a[4]] For the domain, {a[1] = 0, 1 <= a[2], 1 <= a[3], 1 <= a[4], a[5] = 3} The value of the game = , [{f[1](0, a[2], a[3], a[4], 2, 0) + [0], f[2](0, a[2] - 1, a[3] + 1, a[4], 3), f[2](0, a[2], a[3], a[4] - 1, 4), f[2](0, a[2], a[3] - 1, a[4] + 1, 3)}, {}] = , [{[-1 + 3 a[2] + 2 a[3] + a[4]], [{[ {[4 a[2] + 3 a[3] + 2 a[4]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}] }, {[3 a[2] + 2 a[3] + a[4]]}]}, {}] = , [3 a[2] + 2 a[3] + a[4]] For the domain, {a[1] = 0, 1 <= a[2], 4 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[1](0, a[2], a[3], a[4], a[5] - 1, 0) + [0], f[2](0, a[2], a[3] - 1, a[4] + 1, a[5]), f[2](0, a[2], a[3], a[4] - 1, a[5] + 1), f[2](0, a[2] - 1, a[3] + 1, a[4], a[5])}, {}] = , [{[{[{[-3 + 4 a[2] + 3 a[3] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + 2 a[3] + a[4]]}]}, {[3 a[2] + 2 a[3] + a[4]]}] , [-1 + 3 a[2] + 2 a[3] + a[4]]}, {}] = , [3 a[2] + 2 a[3] + a[4]] For the domain, {a[1] = 0, 1 <= a[2], a[4] = 0, 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](0, a[2], a[3], 0, 1, 0) + [0], f[2](0, a[2], a[3] - 1, 1, 2), f[2](0, a[2] - 1, a[3] + 1, 0, 2)}, {}] = , [{[-1 + 3 a[2] + 2 a[3]]}, {}] = , [3 a[2] + 2 a[3]] For the domain, {a[1] = 0, 1 <= a[2], a[4] = 0, 1 <= a[3], a[5] = 3} The value of the game = , [{f[1](0, a[2], a[3], 0, 2, 0) + [0], f[2](0, a[2], a[3] - 1, 1, 3), f[2](0, a[2] - 1, a[3] + 1, 0, 3)}, {}] = , [{[{[{[4 a[2] + 3 a[3]]}, {[3 a[2] + 2 a[3] + 1]}]}, {[3 a[2] + 2 a[3]]}], [-1 + 3 a[2] + 2 a[3]]}, {}] = , [3 a[2] + 2 a[3]] For the domain, {a[1] = 0, 1 <= a[2], 4 <= a[5], a[4] = 0, 1 <= a[3]} The value of the game = , [{ f[1](0, a[2], a[3], 0, a[5] - 1, 0) + [0], f[2](0, a[2] - 1, a[3] + 1, 0, a[5]), f[2](0, a[2], a[3] - 1, 1, a[5])}, {}] = , [{[-1 + 3 a[2] + 2 a[3]], [ {[{[-3 + 4 a[2] + 3 a[3] + a[5]]}, {[1 + 3 a[2] + 2 a[3]]}]}, {[3 a[2] + 2 a[3]]}]}, {}] = , [3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 1, a[5] = 2} The value of the game = , [{f[1](0, a[2], 0, 1, 1, 0) + [0], f[2](0, a[2] - 1, 1, 1, 2), f[2](0, a[2], 0, 0, 3)}, {}] = , [{[3 a[2]]}, {}] = , [3 a[2] + 1] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 2 <= a[4], a[5] = 2} The value of the game = , [{f[1](0, a[2], 0, a[4], 1, 0) + [0], f[2](0, a[2], 0, a[4] - 1, 3), f[2](0, a[2] - 1, 1, a[4], 2)} , {}] = , [{[{[3 a[2] + a[4]]}, {[3 a[2] + a[4]]}], [-1 + 3 a[2] + a[4]] }, {}] = , [3 a[2] + a[4]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 1 <= a[4], a[5] = 3} The value of the game = , [{f[1](0, a[2], 0, a[4], 2, 0) + [0], f[2](0, a[2], 0, a[4] - 1, 4), f[2](0, a[2] - 1, 1, a[4], 3)} , {}] = , [{[-1 + 3 a[2] + a[4]], [ {[{[4 a[2] + 2 a[4]]}, {[1 + 3 a[2] + a[4]]}]}, {[3 a[2] + a[4]]}]}, {}] = , [3 a[2] + a[4]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 4 <= a[5], 1 <= a[4]} The value of the game = , [{ f[1](0, a[2], 0, a[4], a[5] - 1, 0) + [0], f[2](0, a[2] - 1, 1, a[4], a[5]), f[2](0, a[2], 0, a[4] - 1, a[5] + 1)}, {}] = , [{[-1 + 3 a[2] + a[4]], [ {[{[-3 + 4 a[2] + 2 a[4] + a[5]]}, {[1 + 3 a[2] + a[4]]}]}, {[3 a[2] + a[4]]}]}, {}] = , [3 a[2] + a[4]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, a[5] = 2} The value of the game = , [ {f[1](0, a[2], 0, 0, 1, 0) + [0], f[2](0, a[2] - 1, 1, 0, 2)} , {}] = , [{[-1 + 3 a[2]]}, {}] = , [3 a[2]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0, a[5] = 3} The value of the game = , [ {f[1](0, a[2], 0, 0, 2, 0) + [0], f[2](0, a[2] - 1, 1, 0, 3)} , {}] = , [{[{[3 a[2]]}, {[3 a[2]]}], [-1 + 3 a[2]]}, {}] = , [3 a[2]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 4 <= a[5], a[4] = 0} The value of the game = , [{f[1](0, a[2], 0, 0, a[5] - 1, 0) + [0], f[2](0, a[2] - 1, 1, 0, a[5])}, {}] = , [{[{[{[-3 + 4 a[2] + a[5]]}, {[3 a[2] + 1]}]}, {[3 a[2]]}], [-1 + 3 a[2]]}, {}] = , [3 a[2]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 1, 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](0, 0, a[3], 1, 1, 0) + [0], f[2](0, 0, a[3] - 1, 2, 2), f[2](0, 0, a[3], 0, 3)}, {}] = , [{[2 a[3]], [{[2 a[3] + 1]}, {[2 a[3] + 1]}]}, {}] = , [2 a[3] + 1] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[4], 1 <= a[3], a[5] = 2} The value of the game = , [{f[1](0, 0, a[3], a[4], 1, 0) + [0], f[2](0, 0, a[3] - 1, a[4] + 1, 2), f[2](0, 0, a[3], a[4] - 1, 3)}, {}] = , [{[-1 + 2 a[3] + a[4]], [{[2 a[3] + a[4]]}, {[2 a[3] + a[4]]}] }, {}] = , [2 a[3] + a[4]] For the domain, {a[1] = 0, a[2] = 0, 1 <= a[3], 1 <= a[4], a[5] = 3} The value of the game = , [{f[1](0, 0, a[3], a[4], 2, 0) + [0], f[2](0, 0, a[3] - 1, a[4] + 1, 3), f[2](0, 0, a[3], a[4] - 1, 4)}, {}] = , [{[{[{[3 a[3] + 2 a[4]]}, {[1 + 2 a[3] + a[4]]}]}, {[2 a[3] + a[4]]}], [-1 + 2 a[3] + a[4]]}, {}] = , [2 a[3] + a[4]] For the domain, {a[1] = 0, a[2] = 0, 4 <= a[5], 1 <= a[3], 1 <= a[4]} The value of the game = , [{ f[1](0, 0, a[3], a[4], a[5] - 1, 0) + [0], f[2](0, 0, a[3], a[4] - 1, a[5] + 1), f[2](0, 0, a[3] - 1, a[4] + 1, a[5])}, {}] = , [{[{[{[-3 + 3 a[3] + 2 a[4] + a[5]]}, {[1 + 2 a[3] + a[4]]}]}, {[2 a[3] + a[4]]}], [-1 + 2 a[3] + a[4]]}, {}] = , [2 a[3] + a[4]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, 1 <= a[3], a[5] = 2} The value of the game = , [ {f[1](0, 0, a[3], 0, 1, 0) + [0], f[2](0, 0, a[3] - 1, 1, 2)} , {}] = , [{[-1 + 2 a[3]]}, {}] = , [2 a[3]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 0, 1 <= a[3], a[5] = 3} The value of the game = , [ {f[1](0, 0, a[3], 0, 2, 0) + [0], f[2](0, 0, a[3] - 1, 1, 3)} , {}] = , [{[-1 + 2 a[3]], [{[{[3 a[3]]}, {[1 + 2 a[3]]}]}, {[2 a[3]]}]} , {}] = , [2 a[3]] For the domain, {a[1] = 0, a[2] = 0, 4 <= a[5], a[4] = 0, 1 <= a[3]} The value of the game = , [{f[1](0, 0, a[3], 0, a[5] - 1, 0) + [0], f[2](0, 0, a[3] - 1, 1, a[5])}, {}] = , [{[-1 + 2 a[3]], [{[{[-3 + 3 a[3] + a[5]]}, {[1 + 2 a[3]]}]}, {[2 a[3]]}]}, {} ] = , [2 a[3]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 1, a[5] = 2} The value of the game = , [{f[1](0, 0, 0, 1, 1, 0) + [0], f[2](0, 0, 0, 0, 3)}, {}] = , [{[0]}, {}] = , [1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 2 <= a[4], a[5] = 2} The value of the game = , [ {f[1](0, 0, 0, a[4], 1, 0) + [0], f[2](0, 0, 0, a[4] - 1, 3)} , {}] = , [{[{[a[4]]}, {[a[4]]}], [a[4] - 1]}, {}] = , [a[4]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 1 <= a[4], a[5] = 3} The value of the game = , [ {f[1](0, 0, 0, a[4], 2, 0) + [0], f[2](0, 0, 0, a[4] - 1, 4)} , {}] = , [{[{[{[2 a[4]]}, {[a[4] + 1]}]}, {[a[4]]}], [a[4] - 1]}, {}] = , [a[4]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 4 <= a[5], 1 <= a[4]} The value of the game = , [{f[1](0, 0, 0, a[4], a[5] - 1, 0) + [0], f[2](0, 0, 0, a[4] - 1, a[5] + 1)}, {}] = , [{[{[{[-3 + 2 a[4] + a[5]]}, {[a[4] + 1]}]}, {[a[4]]}], [a[4] - 1]}, {}] = , [a[4]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0, a[5] = 2} The value of the game = , [{f[1](0, 0, 0, 0, 1, 0) + [0]}, {}] = , [{[-3]}, {}] = , [0] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0, a[5] = 3} The value of the game = , [{f[1](0, 0, 0, 0, 2, 0) + [0]}, {}] = , [{[-1]}, {}] = , [0] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 4 <= a[5], a[4] = 0} The value of the game = , [{f[1](0, 0, 0, 0, a[5] - 1, 0) + [0]}, {}] = , [{[{[{[a[5] - 3]}, {[1]}]}, {[0]}]}, {}] = , [0] ########## #, f[3], # ########## For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 0} The value of the game = , [ {f[3](a[1] - 1, a[2] + 1, 0, 0), f[3](a[1], a[2] - 1, 1, 0)}, {f[4](a[1], a[2], 0) + [0]}] = , [{[{[4 a[1] + 3 a[2] - 3]}, {[4 a[1] + 3 a[2] - 3]}], [4 a[1] - 4 + 3 a[2]]}, {[4 a[1] + 3 a[2] - 2]}] = , [4 a[1] + 3 a[2] - 3] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 0} The value of the game = , [{f[3](a[1] - 1, 1, 0, 0)}, {f[4](a[1], 0, 0) + [0]}] = , [{[4 a[1] - 4]}, {[4 a[1] - 2]}] = , [4 a[1] - 3] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 0} The value of the game = , [{f[3](0, a[2] - 1, 1, 0)}, {f[4](0, a[2], 0) + [0]}] = , [{[{[-3 + 3 a[2]]}, {[-3 + 3 a[2]]}]}, {[-2 + 3 a[2]]}] = , [-3 + 3 a[2]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 0} The value of the game = , [{}, {f[4](0, 0, 0) + [0]}] = , [{}, {[-2]}] = , [-3] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 0, 1 <= a[3]} The value of the game = , [{f[3](a[1] - 1, a[2] + 1, a[3], 0), f[3](a[1], a[2] - 1, a[3] + 1, 0), f[3](a[1], a[2], a[3] - 1, 1)}, {f[4](a[1], a[2], a[3]) + [0]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 2], [ {[4 a[1] - 3 + 3 a[2] + 2 a[3]]}, {[4 a[1] - 3 + 3 a[2] + 2 a[3]]}]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}] For the domain, {a[2] = 0, 1 <= a[1], a[4] = 0, 1 <= a[3]} The value of the game = , [ {f[3](a[1], 0, a[3] - 1, 1), f[3](a[1] - 1, 1, a[3], 0)}, {f[4](a[1], 0, a[3]) + [0]}] = , [{[{[4 a[1] - 3 + 2 a[3]]}, {[4 a[1] - 3 + 2 a[3]]}], [4 a[1] - 2 + 2 a[3]]}, {[4 a[1] - 2 + 2 a[3]]}] = , [{[4 a[1] - 2 + 2 a[3]]}, {[4 a[1] - 2 + 2 a[3]]}] For the domain, {a[1] = 0, 1 <= a[2], a[4] = 0, 1 <= a[3]} The value of the game = , [ {f[3](0, a[2], a[3] - 1, 1), f[3](0, a[2] - 1, a[3] + 1, 0)}, {f[4](0, a[2], a[3]) + [0]}] = , [{[{[-3 + 3 a[2] + 2 a[3]]}, {[-3 + 3 a[2] + 2 a[3]]}], [-2 + 3 a[2] + 2 a[3]]}, {[-2 + 3 a[2] + 2 a[3]]}] = , [{[-2 + 3 a[2] + 2 a[3]]}, {[-2 + 3 a[2] + 2 a[3]]}] For the domain, {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)}, {f[4](0, 0, a[3]) + [0]}] = , [{[-2 + 2 a[3]]}, {[-2 + 2 a[3]]}] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 1, 1 <= a[3]} The value of the game = , [{f[2](a[1], a[2], a[3], 0, 0) + [1], f[3](a[1] - 1, a[2] + 1, a[3], 1), f[3](a[1], a[2] - 1, a[3] + 1, 1), f[3](a[1], a[2], a[3] - 1, 2)}, {f[4](a[1], a[2], a[3]) + [3]}] = , [{[4 a[1] + 3 a[2] + 2 a[3] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}] = , [4 a[1] + 3 a[2] + 2 a[3]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 1} The value of the game = , [{f[2](a[1], a[2], 0, 0, 0) + [1], f[3](a[1], a[2] - 1, 1, 1), f[3](a[1] - 1, a[2] + 1, 0, 1)}, {f[4](a[1], a[2], 0) + [3]}] = , [{[{[4 a[1] + 3 a[2] - 2]}, {[4 a[1] + 3 a[2] - 2]}], [4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] + 1]}] = , [4 a[1] + 3 a[2]] For the domain, {a[2] = 0, 1 <= a[1], a[4] = 1, 1 <= a[3]} The value of the game = , [{f[2](a[1], 0, a[3], 0, 0) + [1], f[3](a[1], 0, a[3] - 1, 2), f[3](a[1] - 1, 1, a[3], 1)}, {f[4](a[1], 0, a[3]) + [3]}] = , [{[4 a[1] - 1 + 2 a[3]]}, {[4 a[1] + 1 + 2 a[3]]}] = , [4 a[1] + 2 a[3]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 1} The value of the game = , [ {f[2](a[1], 0, 0, 0, 0) + [1], f[3](a[1] - 1, 1, 0, 1)}, {f[4](a[1], 0, 0) + [3]}] = , [{[4 a[1] - 1], [4 a[1] - 3]}, {[4 a[1] + 1]}] = , [4 a[1]] For the domain, {a[1] = 0, 1 <= a[2], a[4] = 1, 1 <= a[3]} The value of the game = , [{f[2](0, a[2], a[3], 0, 0) + [1], f[3](0, a[2], a[3] - 1, 2), f[3](0, a[2] - 1, a[3] + 1, 1)}, {f[4](0, a[2], a[3]) + [3]}] = , [{[-1 + 3 a[2] + 2 a[3]]}, {[1 + 3 a[2] + 2 a[3]]}] = , [3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 1} The value of the game = , [ {f[2](0, a[2], 0, 0, 0) + [1], f[3](0, a[2] - 1, 1, 1)}, {f[4](0, a[2], 0) + [3]}] = , [{[{[-2 + 3 a[2]]}, {[-2 + 3 a[2]]}], [-1 + 3 a[2]]}, {[1 + 3 a[2]]}] = , [3 a[2]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 1, 1 <= a[3]} The value of the game = , [ {f[2](0, 0, a[3], 0, 0) + [1], f[3](0, 0, a[3] - 1, 2)}, {f[4](0, 0, a[3]) + [3]}] = , [{[-1 + 2 a[3]]}, {[1 + 2 a[3]]}] = , [2 a[3]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 1} The value of the game = , [{f[2](0, 0, 0, 0, 0) + [1]}, {f[4](0, 0, 0) + [3]}] = , [{[-3]}, {[1]}] = , [0] For the domain, {1 <= a[2], 1 <= a[1], a[4] = 2, 1 <= a[3]} The value of the game = , [{f[2](a[1], a[2], a[3], 1, 0) + [1], f[3](a[1], a[2] - 1, a[3] + 1, 2), f[3](a[1], a[2], a[3] - 1, 3), f[3](a[1] - 1, a[2] + 1, a[3], 2)}, {}] = , [{[4 a[1] + 3 a[2] + 2 a[3]], [ {[4 a[1] + 3 a[2] + 2 a[3] + 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + 1]}]}, {}] = , [4 a[1] + 3 a[2] + 2 a[3] + 1] For the domain, {1 <= a[2], 1 <= a[1], 3 <= a[4], 1 <= a[3]} The value of the game = , [{ f[2](a[1], a[2], a[3], a[4] - 1, 0) + [1], f[3](a[1] - 1, a[2] + 1, a[3], a[4]), f[3](a[1], a[2], a[3] - 1, a[4] + 1), f[3](a[1], a[2] - 1, a[3] + 1, a[4])}, {}] = , [{[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 2], [ {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}, {[4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1]}]}, {}] = , [4 a[1] + 3 a[2] + 2 a[3] + a[4] - 1] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], a[4] = 2} The value of the game = , [{f[2](a[1], a[2], 0, 1, 0) + [1], f[3](a[1] - 1, a[2] + 1, 0, 2), f[3](a[1], a[2] - 1, 1, 2)}, {}] = , [{[4 a[1] + 3 a[2]]}, {}] = , [4 a[1] + 3 a[2] + 1] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[2](a[1], a[2], 0, a[4] - 1, 0) + [1], f[3](a[1], a[2] - 1, 1, a[4]), f[3](a[1] - 1, a[2] + 1, 0, a[4])}, {}] = , [{[{[4 a[1] + 3 a[2] - 1 + a[4]]}, {[4 a[1] + 3 a[2] - 1 + a[4]]}], [4 a[1] + 3 a[2] - 2 + a[4]] }, {}] = , [4 a[1] + 3 a[2] - 1 + a[4]] For the domain, {a[2] = 0, 1 <= a[1], a[4] = 2, 1 <= a[3]} The value of the game = , [{f[2](a[1], 0, a[3], 1, 0) + [1], f[3](a[1], 0, a[3] - 1, 3), f[3](a[1] - 1, 1, a[3], 2)}, {}] = , [{[4 a[1] + 2 a[3]], [{[4 a[1] + 1 + 2 a[3]]}, {[4 a[1] + 1 + 2 a[3]]}]}, {}] = , [4 a[1] + 1 + 2 a[3]] For the domain, {a[2] = 0, 1 <= a[1], 3 <= a[4], 1 <= a[3]} The value of the game = , [{f[2](a[1], 0, a[3], a[4] - 1, 0) + [1], f[3](a[1] - 1, 1, a[3], a[4]), f[3](a[1], 0, a[3] - 1, a[4] + 1)}, {}] = , [{[{[4 a[1] - 1 + 2 a[3] + a[4]]}, {[4 a[1] - 1 + 2 a[3] + a[4]]}], [4 a[1] - 2 + 2 a[3] + a[4]] }, {}] = , [4 a[1] - 1 + 2 a[3] + a[4]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], a[4] = 2} The value of the game = , [{f[2](a[1], 0, 0, 1, 0) + [1], f[3](a[1] - 1, 1, 0, 2)}, {}] = , [{[4 a[1]]}, {}] = , [4 a[1] + 1] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1], 3 <= a[4]} The value of the game = , [{f[2](a[1], 0, 0, a[4] - 1, 0) + [1], f[3](a[1] - 1, 1, 0, a[4])}, {}] = , [{[4 a[1] - 2 + a[4]], [{[4 a[1] - 1 + a[4]]}, {[4 a[1] - 1 + a[4]]}]}, {}] = , [4 a[1] - 1 + a[4]] For the domain, {a[1] = 0, 1 <= a[2], a[4] = 2, 1 <= a[3]} The value of the game = , [{f[2](0, a[2], a[3], 1, 0) + [1], f[3](0, a[2], a[3] - 1, 3), f[3](0, a[2] - 1, a[3] + 1, 2)}, {}] = , [{[3 a[2] + 2 a[3]], [{[1 + 3 a[2] + 2 a[3]]}, {[1 + 3 a[2] + 2 a[3]]}]}, {}] = , [1 + 3 a[2] + 2 a[3]] For the domain, {a[1] = 0, 1 <= a[2], 3 <= a[4], 1 <= a[3]} The value of the game = , [{f[2](0, a[2], a[3], a[4] - 1, 0) + [1], f[3](0, a[2] - 1, a[3] + 1, a[4]), f[3](0, a[2], a[3] - 1, a[4] + 1)}, {}] = , [{[-2 + 3 a[2] + 2 a[3] + a[4]], [ {[-1 + 3 a[2] + 2 a[3] + a[4]]}, {[-1 + 3 a[2] + 2 a[3] + a[4]]}]}, {}] = , [-1 + 3 a[2] + 2 a[3] + a[4]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], a[4] = 2} The value of the game = , [{f[2](0, a[2], 0, 1, 0) + [1], f[3](0, a[2] - 1, 1, 2)}, {}] = , [{[3 a[2]]}, {}] = , [1 + 3 a[2]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2], 3 <= a[4]} The value of the game = , [{f[2](0, a[2], 0, a[4] - 1, 0) + [1], f[3](0, a[2] - 1, 1, a[4])}, {}] = , [{[{[-1 + 3 a[2] + a[4]]}, {[-1 + 3 a[2] + a[4]]}], [-2 + 3 a[2] + a[4]]}, {}] = , [-1 + 3 a[2] + a[4]] For the domain, {a[1] = 0, a[2] = 0, a[4] = 2, 1 <= a[3]} The value of the game = , [{f[2](0, 0, a[3], 1, 0) + [1], f[3](0, 0, a[3] - 1, 3)}, {}] = , [{[2 a[3]], [{[1 + 2 a[3]]}, {[1 + 2 a[3]]}]}, {}] = , [1 + 2 a[3]] For the domain, {a[1] = 0, a[2] = 0, 3 <= a[4], 1 <= a[3]} The value of the game = , [{f[2](0, 0, a[3], a[4] - 1, 0) + [1], f[3](0, 0, a[3] - 1, a[4] + 1)}, {}] = , [{[-2 + 2 a[3] + a[4]], [{[-1 + 2 a[3] + a[4]]}, {[-1 + 2 a[3] + a[4]]}]}, {}] = , [-1 + 2 a[3] + a[4]] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, a[4] = 2} The value of the game = , [{f[2](0, 0, 0, 1, 0) + [1]}, {}] = , [{[0]}, {}] = , [1] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0, 3 <= a[4]} The value of the game = , [{f[2](0, 0, 0, a[4] - 1, 0) + [1]}, {}] = , [{[{[a[4] - 1]}, {[a[4] - 1]}]}, {}] = , [a[4] - 1] ########## #, f[4], # ########## For the domain, {1 <= a[2], a[3] = 1, 1 <= a[1]} The value of the game = , [{f[3](a[1], a[2], 0, 0) + [2], f[4](a[1] - 1, a[2] + 1, 1), f[4](a[1], a[2] - 1, 2)}, {f[5](a[1], a[2]) + [4]}] = , [{[4 a[1] + 3 a[2] - 1]}, {[4 a[1] + 3 a[2] + 3]}] = , [4 a[1] + 3 a[2]] For the domain, {a[3] = 0, 1 <= a[2], 1 <= a[1]} The value of the game = , [ {f[4](a[1], a[2] - 1, 1), f[4](a[1] - 1, a[2] + 1, 0)}, {f[5](a[1], a[2]) + [0]}] = , [{[4 a[1] + 3 a[2] - 3]}, {[4 a[1] + 3 a[2] - 1]}] = , [4 a[1] + 3 a[2] - 2] For the domain, {a[2] = 0, a[3] = 1, 1 <= a[1]} The value of the game = , [ {f[3](a[1], 0, 0, 0) + [2], f[4](a[1] - 1, 1, 1)}, {f[5](a[1], 0) + [4]}] = , [{[4 a[1] - 1]}, {[4 a[1] + 3]}] = , [4 a[1]] For the domain, {a[3] = 0, a[2] = 0, 1 <= a[1]} The value of the game = , [{f[4](a[1] - 1, 1, 0)}, {f[5](a[1], 0) + [0]}] = , [{[4 a[1] - 3]}, {[4 a[1] - 1]}] = , [4 a[1] - 2] For the domain, {a[1] = 0, 1 <= a[2], a[3] = 1} The value of the game = , [ {f[3](0, a[2], 0, 0) + [2], f[4](0, a[2] - 1, 2)}, {f[5](0, a[2]) + [4]}] = , [{[-1 + 3 a[2]]}, {[3 + 3 a[2]]}] = , [3 a[2]] For the domain, {a[1] = 0, a[3] = 0, 1 <= a[2]} The value of the game = , [{f[4](0, a[2] - 1, 1)}, {f[5](0, a[2]) + [0]}] = , [{[-3 + 3 a[2]]}, {[-1 + 3 a[2]]}] = , [-2 + 3 a[2]] For the domain, {a[1] = 0, a[2] = 0, a[3] = 1} The value of the game = , [{f[3](0, 0, 0, 0) + [2]}, {f[5](0, 0) + [4]}] = , [{[-1]}, {[3]}] = , [0] For the domain, {a[1] = 0, a[3] = 0, a[2] = 0} The value of the game = , [{}, {f[5](0, 0) + [0]}] = , [{}, {[-1]}] = , [-2] For the domain, {1 <= a[2], 2 <= a[3], 1 <= a[1]} The value of the game = , [{f[3](a[1], a[2], a[3] - 1, 0) + [2], f[4](a[1] - 1, a[2] + 1, a[3]), f[4](a[1], a[2] - 1, a[3] + 1)}, {}] = , [{[{[4 a[1] + 3 a[2] + 2 a[3] - 2]}, {[4 a[1] + 3 a[2] + 2 a[3] - 2]}], [4 a[1] - 3 + 3 a[2] + 2 a[3]]}, {}] = , [4 a[1] + 3 a[2] + 2 a[3] - 2] For the domain, {a[2] = 0, 2 <= a[3], 1 <= a[1]} The value of the game = , [ {f[3](a[1], 0, a[3] - 1, 0) + [2], f[4](a[1] - 1, 1, a[3])}, {}] = , [{[4 a[1] - 3 + 2 a[3]], [{[4 a[1] - 2 + 2 a[3]]}, {[4 a[1] - 2 + 2 a[3]]}]}, {}] = , [4 a[1] - 2 + 2 a[3]] For the domain, {a[1] = 0, 1 <= a[2], 2 <= a[3]} The value of the game = , [{ f[3](0, a[2], a[3] - 1, 0) + [2], f[4](0, a[2] - 1, a[3] + 1) }, {}] = , [{[{[-2 + 3 a[2] + 2 a[3]]}, {[-2 + 3 a[2] + 2 a[3]]}], [-3 + 3 a[2] + 2 a[3]]}, {}] = , [-2 + 3 a[2] + 2 a[3]] For the domain, {a[1] = 0, a[2] = 0, 2 <= a[3]} The value of the game = , [{f[3](0, 0, a[3] - 1, 0) + [2]}, {}] = , [{[{[-2 + 2 a[3]]}, {[-2 + 2 a[3]]}]}, {}] = , [-2 + 2 a[3]] ########## #, f[5], # ########## For the domain, {a[2] = 1, 1 <= a[1]} The value of the game = , [ {f[4](a[1], 0, 0) + [3], f[5](a[1] - 1, 2)}, {f[6](a[1]) + [5]}] = , [{[4 a[1] + 1]}, {[4 a[1] + 5]}] = , [4 a[1] + 2] For the domain, {a[2] = 0, 1 <= a[1]} The value of the game = , [{f[5](a[1] - 1, 1)}, {f[6](a[1]) + [0]}] = , [{[4 a[1] - 2]}, {[4 a[1]]}] = , [4 a[1] - 1] For the domain, {a[1] = 0, a[2] = 1} The value of the game = , [{f[4](0, 0, 0) + [3]}, {f[6](0) + [5]}] = , [{[1]}, {[5]}] = , [2] For the domain, {a[1] = 0, a[2] = 0} The value of the game = , [{}, {f[6](0) + [0]}] = , [{}, {[0]}] = , [-1] For the domain, {2 <= a[2], 1 <= a[1]} The value of the game = , [ {f[4](a[1], a[2] - 1, 0) + [3], f[5](a[1] - 1, a[2] + 1)}, {} ] = , [{[4 a[1] + 3 a[2] - 2]}, {}] = , [4 a[1] + 3 a[2] - 1] For the domain, {a[1] = 0, 2 <= a[2]} The value of the game = , [{f[4](0, a[2] - 1, 0) + [3]}, {}] = , [{[-2 + 3 a[2]]}, {}] = , [-1 + 3 a[2]] ########## #, f[6], # ########## For the domain, {1 <= a[1]} The value of the game = , [{f[5](a[1] - 1, 0) + [4]}, {}] = , [{[4 a[1] - 1]}, {}] = , [4 a[1]] For the domain, {a[1] = 0} The value of the game = , [{}, {}] = , [{}, {}] = , [0] ###The conjectures is proved### >