/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__U11(tt()) -> a__U12(tt()) a__U12(tt()) -> tt() a__isNePal(__(I,__(P,I))) -> a__U11(tt()) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U12(X)) -> a__U12(mark(X)) mark(isNePal(X)) -> a__isNePal(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 4x0, [U12](x0) = 2x0, [U11](x0) = x0, [a__isNePal](x0) = 4x0, [a__U12](x0) = 2x0, [a__U11](x0) = x0, [tt] = 0, [nil] = 4, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = X + 4 >= X = mark(X) a____(nil(),X) = X + 4 >= X = mark(X) a__U11(tt()) = 0 >= 0 = a__U12(tt()) a__U12(tt()) = 0 >= 0 = tt() a__isNePal(__(I,__(P,I))) = 8I + 4P >= 0 = a__U11(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = X >= X = a__U11(mark(X)) mark(U12(X)) = 2X >= 2X = a__U12(mark(X)) mark(isNePal(X)) = 4X >= 4X = a__isNePal(mark(X)) mark(nil()) = 4 >= 4 = nil() mark(tt()) = 0 >= 0 = tt() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X) = X >= X = U11(X) a__U12(X) = 2X >= 2X = U12(X) a__isNePal(X) = 4X >= 4X = isNePal(X) problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) -> a__U12(tt()) a__U12(tt()) -> tt() a__isNePal(__(I,__(P,I))) -> a__U11(tt()) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U12(X)) -> a__U12(mark(X)) mark(isNePal(X)) -> a__isNePal(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0 + 4, [U12](x0) = 2x0 + 4, [U11](x0) = x0 + 4, [a__isNePal](x0) = x0 + 4, [a__U12](x0) = 2x0 + 4, [a__U11](x0) = x0 + 4, [tt] = 0, [nil] = 1, [mark](x0) = x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) = 4 >= 4 = a__U12(tt()) a__U12(tt()) = 4 >= 0 = tt() a__isNePal(__(I,__(P,I))) = 2I + P + 4 >= 4 = a__U11(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = X + 4 >= X + 4 = a__U11(mark(X)) mark(U12(X)) = 2X + 4 >= 2X + 4 = a__U12(mark(X)) mark(isNePal(X)) = X + 4 >= X + 4 = a__isNePal(mark(X)) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X) = X + 4 >= X + 4 = U11(X) a__U12(X) = 2X + 4 >= 2X + 4 = U12(X) a__isNePal(X) = X + 4 >= X + 4 = isNePal(X) problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) -> a__U12(tt()) a__isNePal(__(I,__(P,I))) -> a__U11(tt()) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U12(X)) -> a__U12(mark(X)) mark(isNePal(X)) -> a__isNePal(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 2x0, [U12](x0) = x0, [U11](x0) = 4x0, [a__isNePal](x0) = 2x0, [a__U12](x0) = x0, [a__U11](x0) = 4x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [a____](x0, x1) = 4x0 + x1 + 4, [__](x0, x1) = 4x0 + x1 + 4 orientation: a____(__(X,Y),Z) = 16X + 4Y + Z + 20 >= 4X + 4Y + Z + 8 = a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) = 0 >= 0 = a__U12(tt()) a__isNePal(__(I,__(P,I))) = 10I + 8P + 16 >= 0 = a__U11(tt()) mark(__(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = a____(mark(X1),mark(X2)) mark(U11(X)) = 4X >= 4X = a__U11(mark(X)) mark(U12(X)) = X >= X = a__U12(mark(X)) mark(isNePal(X)) = 2X >= 2X = a__isNePal(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() a____(X1,X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(X1,X2) a__U11(X) = 4X >= 4X = U11(X) a__U12(X) = X >= X = U12(X) a__isNePal(X) = 2X >= 2X = isNePal(X) problem: a__U11(tt()) -> a__U12(tt()) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U12(X)) -> a__U12(mark(X)) mark(isNePal(X)) -> a__isNePal(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 2x0, [U12](x0) = x0, [U11](x0) = 2x0, [a__isNePal](x0) = 2x0, [a__U12](x0) = x0, [a__U11](x0) = 2x0, [tt] = 0, [nil] = 0, [mark](x0) = 4x0, [a____](x0, x1) = x0 + x1 + 4, [__](x0, x1) = x0 + x1 + 1 orientation: a__U11(tt()) = 0 >= 0 = a__U12(tt()) mark(__(X1,X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = a____(mark(X1),mark(X2)) mark(U11(X)) = 8X >= 8X = a__U11(mark(X)) mark(U12(X)) = 4X >= 4X = a__U12(mark(X)) mark(isNePal(X)) = 8X >= 8X = a__isNePal(mark(X)) mark(nil()) = 0 >= 0 = nil() mark(tt()) = 0 >= 0 = tt() a____(X1,X2) = X1 + X2 + 4 >= X1 + X2 + 1 = __(X1,X2) a__U11(X) = 2X >= 2X = U11(X) a__U12(X) = X >= X = U12(X) a__isNePal(X) = 2X >= 2X = isNePal(X) problem: a__U11(tt()) -> a__U12(tt()) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U12(X)) -> a__U12(mark(X)) mark(isNePal(X)) -> a__isNePal(mark(X)) mark(nil()) -> nil() mark(tt()) -> tt() a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 4x0 + 4, [U12](x0) = x0 + 4, [U11](x0) = 2x0, [a__isNePal](x0) = 4x0 + 4, [a__U12](x0) = x0 + 4, [a__U11](x0) = 2x0, [tt] = 4, [nil] = 1, [mark](x0) = 4x0, [a____](x0, x1) = 4x0 + x1, [__](x0, x1) = 4x0 + x1 + 4 orientation: a__U11(tt()) = 8 >= 8 = a__U12(tt()) mark(__(X1,X2)) = 16X1 + 4X2 + 16 >= 16X1 + 4X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = 8X >= 8X = a__U11(mark(X)) mark(U12(X)) = 4X + 16 >= 4X + 4 = a__U12(mark(X)) mark(isNePal(X)) = 16X + 16 >= 16X + 4 = a__isNePal(mark(X)) mark(nil()) = 4 >= 1 = nil() mark(tt()) = 16 >= 4 = tt() a__U11(X) = 2X >= 2X = U11(X) a__U12(X) = X + 4 >= X + 4 = U12(X) a__isNePal(X) = 4X + 4 >= 4X + 4 = isNePal(X) problem: a__U11(tt()) -> a__U12(tt()) mark(U11(X)) -> a__U11(mark(X)) a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [a__U12](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [0] [a__U11](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [tt] = [0] [1], [1 0 1] [0] [mark](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1] [0] a__U11(tt()) = [1] >= [1] = a__U12(tt()) [0] [0] [1 0 1] [0] [1 0 1] [0] mark(U11(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__U11(mark(X)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] a__U11(X) = [0 0 0]X + [1] >= [0 0 0]X = U11(X) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] a__U12(X) = [0 0 0]X + [1] >= [0 0 0]X = U12(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] a__isNePal(X) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] problem: mark(U11(X)) -> a__U11(mark(X)) a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [U11](x0) = [0 0 1]x0 + [0] [0 0 1] [1], [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [a__U11](x0) = [0 0 1]x0 + [1] [0 0 1] [1], [1 0 1] [0] [mark](x0) = [1 1 0]x0 + [1] [1 0 1] [0] orientation: [1 0 1] [1] [1 0 1] [0] mark(U11(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = a__U11(mark(X)) [1 0 1] [1] [1 0 1] [1] [1 0 0] [0] [1 0 0] [0] a__U11(X) = [0 0 1]X + [1] >= [0 0 1]X + [0] = U11(X) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1 0 0] a__U12(X) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isNePal(X) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] problem: a__U11(X) -> U11(X) a__U12(X) -> U12(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [a__isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U12(X) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__isNePal(X) = [0 0 0]X + [0] >= [0 0 0]X = isNePal(X) [0 0 0] [0] [0 0 0] problem: a__U11(X) -> U11(X) a__U12(X) -> U12(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [a__U12](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__U12(X) = [0 0 0]X + [0] >= [0 0 0]X = U12(X) [0 0 0] [0] [0 0 0] problem: a__U11(X) -> U11(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [a__U11](x0) = [0 0 0]x0 + [0] [0 0 1] [0] orientation: [1 0 0] [1] [1 0 0] a__U11(X) = [0 0 0]X + [0] >= [0 0 0]X = U11(X) [0 0 1] [0] [0 0 0] problem: Qed