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: [isNePal](x0) = x0 + 4, [U12](x0) = 2x0 + 2, [U11](x0) = 2x0 + 2, [tt] = 4, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 3 orientation: active(__(__(X,Y),Z)) = X + Y + Z + 6 >= X + Y + Z + 6 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 4 >= X = mark(X) active(__(nil(),X)) = X + 4 >= X = mark(X) active(U11(tt())) = 10 >= 10 = mark(U12(tt())) active(U12(tt())) = 10 >= 4 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 2I + P + 10 >= 10 = mark(U11(tt())) mark(__(X1,X2)) = X1 + X2 + 3 >= X1 + X2 + 3 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(U11(X)) = 2X + 2 >= 2X + 2 = active(U11(mark(X))) mark(tt()) = 4 >= 4 = active(tt()) mark(U12(X)) = 2X + 2 >= 2X + 2 = active(U12(mark(X))) mark(isNePal(X)) = X + 4 >= X + 4 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) U11(mark(X)) = 2X + 2 >= 2X + 2 = U11(X) U11(active(X)) = 2X + 2 >= 2X + 2 = U11(X) U12(mark(X)) = 2X + 2 >= 2X + 2 = U12(X) U12(active(X)) = 2X + 2 >= 2X + 2 = U12(X) isNePal(mark(X)) = X + 4 >= X + 4 = isNePal(X) isNePal(active(X)) = X + 4 >= X + 4 = isNePal(X) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(U11(tt())) -> mark(U12(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) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0 + 2, [U12](x0) = x0, [U11](x0) = x0 + 3, [tt] = 4, [nil] = 2, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 3 orientation: active(__(__(X,Y),Z)) = X + Y + Z + 6 >= X + Y + Z + 6 = mark(__(X,__(Y,Z))) active(U11(tt())) = 7 >= 4 = mark(U12(tt())) active(isNePal(__(I,__(P,I)))) = 2I + P + 8 >= 7 = mark(U11(tt())) mark(__(X1,X2)) = X1 + X2 + 3 >= X1 + X2 + 3 = active(__(mark(X1),mark(X2))) mark(nil()) = 2 >= 2 = active(nil()) mark(U11(X)) = X + 3 >= X + 3 = active(U11(mark(X))) mark(tt()) = 4 >= 4 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNePal(X)) = X + 2 >= X + 2 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 3 >= X1 + X2 + 3 = __(X1,X2) U11(mark(X)) = X + 3 >= X + 3 = U11(X) U11(active(X)) = X + 3 >= X + 3 = U11(X) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNePal(mark(X)) = X + 2 >= X + 2 = isNePal(X) isNePal(active(X)) = X + 2 >= X + 2 = isNePal(X) 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) DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> U11#(mark(X)) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> U12#(mark(X)) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> isNePal#(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) TRS: 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) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> U11#(mark(X)) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> U12#(mark(X)) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> isNePal#(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) TRS: 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) graph: isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(active(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) -> isNePal#(active(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) U12#(mark(X)) -> U12#(X) -> U12#(active(X)) -> U12#(X) U12#(mark(X)) -> U12#(X) -> U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) -> U12#(active(X)) -> U12#(X) U12#(active(X)) -> U12#(X) -> U12#(mark(X)) -> U12#(X) U11#(mark(X)) -> U11#(X) -> U11#(active(X)) -> U11#(X) U11#(mark(X)) -> U11#(X) -> U11#(mark(X)) -> U11#(X) U11#(active(X)) -> U11#(X) -> U11#(active(X)) -> U11#(X) U11#(active(X)) -> U11#(X) -> U11#(mark(X)) -> U11#(X) mark#(isNePal(X)) -> isNePal#(mark(X)) -> isNePal#(active(X)) -> isNePal#(X) mark#(isNePal(X)) -> isNePal#(mark(X)) -> isNePal#(mark(X)) -> isNePal#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNePal(X)) -> mark#(X) -> mark#(U12(X)) -> U12#(mark(X)) mark#(isNePal(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(isNePal(X)) -> mark#(X) -> mark#(U11(X)) -> U11#(mark(X)) mark#(isNePal(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(U12(X)) -> U12#(mark(X)) -> U12#(active(X)) -> U12#(X) mark#(U12(X)) -> U12#(mark(X)) -> U12#(mark(X)) -> U12#(X) mark#(U12(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U12(X)) -> mark#(X) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> U12#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(U12(X)) -> mark#(X) -> mark#(U11(X)) -> U11#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(U11(X)) -> U11#(mark(X)) -> U11#(active(X)) -> U11#(X) mark#(U11(X)) -> U11#(mark(X)) -> U11#(mark(X)) -> U11#(X) mark#(U11(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U11(X)) -> mark#(X) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(U11(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(U11(X)) -> mark#(X) -> mark#(U12(X)) -> U12#(mark(X)) mark#(U11(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(U11(X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(U11(X)) -> mark#(X) -> mark#(U11(X)) -> U11#(mark(X)) mark#(U11(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(tt()) -> active#(tt()) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(tt()) -> active#(tt()) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(tt()) -> active#(tt()) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(nil()) -> active#(nil()) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(nil()) -> active#(nil()) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> U12#(mark(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U11(X)) -> U11#(mark(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> U12#(mark(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U11(X)) -> U11#(mark(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(X1,active(X2)) -> __#(X1,X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(active(X1),X2) -> __#(X1,X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(mark(X1),X2) -> __#(X1,X2) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U12(X)) -> U12#(mark(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U12(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(tt()) -> active#(tt()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U11(X)) -> U11#(mark(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U11(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(nil()) -> active#(nil()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(X1,active(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(active(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(X1,active(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(active(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(mark(X1),X2) -> __#(X1,X2) SCC Processor: #sccs: 5 #rules: 22 #arcs: 154/784 DPs: mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNePal(X)) -> active#(isNePal(mark(X))) TRS: 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) EDG Processor: DPs: mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNePal(X)) -> active#(isNePal(mark(X))) TRS: 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) graph: mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(isNePal(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(isNePal(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(isNePal(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U12(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(U12(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(U12(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(U12(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(U11(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(U11(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(U11(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(U11(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(U11(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U11(X)) -> active#(U11(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> active#(U12(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U11(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U12(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) SCC Processor: #sccs: 1 #rules: 10 #arcs: 68/144 DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(U12(X)) -> active#(U12(mark(X))) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) TRS: 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) Semantic Labeling Processor: dimension: 1 usable rules: 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) interpretation: [isNePal](x0) = 0, [U12](x0) = x0, [U11](x0) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = 1, [__](x0, x1) = x1 labeled: usable (for model): argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = 0 pi(nil) = [] pi(tt) = [] pi(U11) = [0] pi(U12) = 0 pi(isNePal) = 0 pi(active#) = 0 pi(mark#) = 0 precedence: mark# ~ active# ~ isNePal ~ U12 ~ U11 ~ tt ~ nil ~ mark ~ active ~ __ problem: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U12(X)) -> active#(U12(mark(X))) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: 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) Restore Modifier: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U12(X)) -> active#(U12(mark(X))) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: 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) SCC Processor: #sccs: 1 #rules: 2 #arcs: 58/36 DPs: mark#(isNePal(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) TRS: 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) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {3} transitions: f680() -> 4* mark{#,0}(4) -> 3* problem: DPs: mark#(isNePal(X)) -> mark#(X) TRS: 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) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: mark{#,0}(2) -> 1* f710() -> 2* problem: DPs: TRS: 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) Qed DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) TRS: 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) Subterm Criterion Processor: simple projection: pi(__#) = 1 problem: DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) TRS: 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) Subterm Criterion Processor: simple projection: pi(__#) = 0 problem: DPs: TRS: 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) Qed DPs: U11#(mark(X)) -> U11#(X) U11#(active(X)) -> U11#(X) TRS: 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) Subterm Criterion Processor: simple projection: pi(U11#) = 0 problem: DPs: TRS: 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) Qed DPs: U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) TRS: 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) Subterm Criterion Processor: simple projection: pi(U12#) = 0 problem: DPs: TRS: 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) Qed DPs: isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) TRS: 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) Subterm Criterion Processor: simple projection: pi(isNePal#) = 0 problem: DPs: TRS: 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) Qed