/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(U12(tt())) active(U12(tt())) -> mark(tt()) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [tt] = 0, [active](x0) = x0, [nil] = 0, [U11](x0) = x0 + 2, [__](x0, x1) = x0 + x1, [isNePal](x0) = 6x0 + 4, [U12](x0) = 2x0 + 2, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt())) = 2 >= 2 = mark(U12(tt())) active(U12(tt())) = 2 >= 0 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 12I + 6P + 4 >= 2 = mark(U11(tt())) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = X + 2 >= X + 2 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 2X + 2 >= 2X + 2 = active(U12(mark(X))) mark(isNePal(X)) = 6X + 4 >= 6X + 4 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X)) = X + 2 >= X + 2 = U11(X) U11(active(X)) = X + 2 >= X + 2 = U11(X) U12(mark(X)) = 2X + 2 >= 2X + 2 = U12(X) U12(active(X)) = 2X + 2 >= 2X + 2 = U12(X) isNePal(mark(X)) = 6X + 4 >= 6X + 4 = isNePal(X) isNePal(active(X)) = 6X + 4 >= 6X + 4 = isNePal(X) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(U12(tt())) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [tt] = 4, [active](x0) = x0, [nil] = 0, [U11](x0) = 4x0, [__](x0, x1) = x0 + x1, [isNePal](x0) = 4x0 + 1, [U12](x0) = x0 + 2, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt())) = 16 >= 6 = mark(U12(tt())) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = 4X >= 4X = active(U11(mark(X))) mark(tt()) = 4 >= 4 = active(tt()) mark(U12(X)) = X + 2 >= X + 2 = active(U12(mark(X))) mark(isNePal(X)) = 4X + 1 >= 4X + 1 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X)) = 4X >= 4X = U11(X) U11(active(X)) = 4X >= 4X = U11(X) U12(mark(X)) = X + 2 >= X + 2 = U12(X) U12(active(X)) = X + 2 >= X + 2 = U12(X) isNePal(mark(X)) = 4X + 1 >= 4X + 1 = isNePal(X) isNePal(active(X)) = 4X + 1 >= 4X + 1 = isNePal(X) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [1 0 0] [active](x0) = [0 0 0]x0 [0 0 1] , [1] [nil] = [0] [0], [1 0 1] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 1] [__](x0, x1) = [0 0 0]x0 + [1 0 0]x1 [0 0 0] [0 0 0] , [1 0 1] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] active(__(X,nil())) = [0 0 0]X + [0] >= [0 0 0]X = mark(X) [0 0 0] [0] [0 0 0] [1 0 1] [1] [1 0 1] active(__(nil(),X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(X) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(__(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 1] [1 0 1] mark(U11(X)) = [0 0 0]X >= [0 0 0]X = active(U11(mark(X))) [0 0 0] [0 0 0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 1] [1 0 1] mark(U12(X)) = [0 0 0]X >= [0 0 0]X = active(U12(mark(X))) [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(isNePal(X)) = [0 0 0]X >= [0 0 0]X = active(isNePal(mark(X))) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] __(mark(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] __(X1,mark(X2)) = [0 0 0]X1 + [1 0 1]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] __(active(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] __(X1,active(X2)) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] U11(mark(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] U12(mark(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] U12(active(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] isNePal(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] isNePal(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 0] [0] [0 0 0] [0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [tt] = 4, [active](x0) = x0, [nil] = 0, [U11](x0) = x0, [__](x0, x1) = 4x0 + x1 + 1, [isNePal](x0) = x0, [U12](x0) = 2x0, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z + 5 >= 4X + 4Y + Z + 2 = mark(__(X,__(Y,Z))) mark(__(X1,X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = X >= X = active(U11(mark(X))) mark(tt()) = 4 >= 4 = active(tt()) mark(U12(X)) = 2X >= 2X = active(U12(mark(X))) mark(isNePal(X)) = X >= X = active(isNePal(mark(X))) __(mark(X1),X2) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = __(X1,X2) U11(mark(X)) = X >= X = U11(X) U11(active(X)) = X >= X = U11(X) U12(mark(X)) = 2X >= 2X = U12(X) U12(active(X)) = 2X >= 2X = U12(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) problem: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [tt] = 4, [active](x0) = x0 + 1, [nil] = 4, [U11](x0) = 3x0 + 2, [__](x0, x1) = 4x0 + x1 + 2, [isNePal](x0) = 4x0 + 1, [U12](x0) = 2x0 + 2, [mark](x0) = 3x0 orientation: mark(__(X1,X2)) = 12X1 + 3X2 + 6 >= 12X1 + 3X2 + 3 = active(__(mark(X1),mark(X2))) mark(nil()) = 12 >= 5 = active(nil()) mark(U11(X)) = 9X + 6 >= 9X + 3 = active(U11(mark(X))) mark(tt()) = 12 >= 5 = active(tt()) mark(U12(X)) = 6X + 6 >= 6X + 3 = active(U12(mark(X))) mark(isNePal(X)) = 12X + 3 >= 12X + 2 = active(isNePal(mark(X))) __(mark(X1),X2) = 12X1 + X2 + 2 >= 4X1 + X2 + 2 = __(X1,X2) __(X1,mark(X2)) = 4X1 + 3X2 + 2 >= 4X1 + X2 + 2 = __(X1,X2) __(active(X1),X2) = 4X1 + X2 + 6 >= 4X1 + X2 + 2 = __(X1,X2) __(X1,active(X2)) = 4X1 + X2 + 3 >= 4X1 + X2 + 2 = __(X1,X2) U11(mark(X)) = 9X + 2 >= 3X + 2 = U11(X) U11(active(X)) = 3X + 5 >= 3X + 2 = U11(X) U12(mark(X)) = 6X + 2 >= 2X + 2 = U12(X) U12(active(X)) = 2X + 4 >= 2X + 2 = U12(X) isNePal(mark(X)) = 12X + 1 >= 4X + 1 = isNePal(X) isNePal(active(X)) = 4X + 5 >= 4X + 1 = isNePal(X) problem: __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U12(mark(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [0 0 0] [0], [1 0 1] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [mark](x0) = [0 1 1]x0 + [0] [0 1 1] [1] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(X1,X2) [0 1 1] [0 0 0] [1] [0 0 1] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 0 0] U11(mark(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] U12(mark(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 1 1] [1] [1 0 1] isNePal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = isNePal(X) [0 0 0] [0] [0 0 0] problem: __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U12(mark(X)) -> U12(X) Matrix Interpretation Processor: dim=1 interpretation: [U11](x0) = x0 + 4, [__](x0, x1) = 4x0 + 2x1 + 4, [U12](x0) = x0, [mark](x0) = 4x0 + 4 orientation: __(mark(X1),X2) = 16X1 + 2X2 + 20 >= 4X1 + 2X2 + 4 = __(X1,X2) __(X1,mark(X2)) = 4X1 + 8X2 + 12 >= 4X1 + 2X2 + 4 = __(X1,X2) U11(mark(X)) = 4X + 8 >= X + 4 = U11(X) U12(mark(X)) = 4X + 4 >= X = U12(X) problem: Qed