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=3 interpretation: [1 0 0] [1] [isNePal](x0) = [0 0 0]x0 + [1] [0 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] , [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] 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 0] [1 0 0] active(__(X,nil())) = [0 0 0]X >= [0 0 0]X = mark(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(__(nil(),X)) = [0 0 0]X >= [0 0 0]X = mark(X) [0 0 0] [0 0 0] [0] [0] active(U11(tt())) = [0] >= [0] = mark(U12(tt())) [0] [0] [0] [0] active(U12(tt())) = [0] >= [0] = mark(tt()) [0] [0] [2 0 0] [1 0 0] [1] [0] active(isNePal(__(I,__(P,I)))) = [0 0 0]I + [0 0 0]P + [0] >= [0] = mark(U11(tt())) [0 0 0] [0 0 0] [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] 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] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 0] [1 0 0] 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 0] [1 0 0] mark(U12(X)) = [0 0 0]X >= [0 0 0]X = active(U12(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNePal(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 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 0 0] [1 0 0] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U12(mark(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U12(active(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] 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 0] [1] [1 0 0] [1] 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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(U12(tt())) active(U12(tt())) -> mark(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=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] [1] [U11](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] 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 0] [1 0 0] active(__(X,nil())) = [0 0 0]X >= [0 0 0]X = mark(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(__(nil(),X)) = [0 0 0]X >= [0 0 0]X = mark(X) [0 0 0] [0 0 0] [1] [0] active(U11(tt())) = [0] >= [0] = mark(U12(tt())) [0] [0] [0] [0] active(U12(tt())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] 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] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 0] [1] [1 0 0] [1] mark(U11(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U11(mark(X))) [0 0 0] [0] [0 0 0] [0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 0] [1 0 0] mark(U12(X)) = [0 0 0]X >= [0 0 0]X = active(U12(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(isNePal(X)) = [0 0 0]X >= [0 0 0]X = active(isNePal(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U11(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U11(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] U12(mark(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U12(active(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(mark(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(active(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(__(X,nil())) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(U12(tt())) -> mark#(tt()) 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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(__(X,nil())) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(U12(tt())) -> mark#(tt()) 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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) 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#(U12(tt())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(nil(),X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(X,nil())) -> mark#(X) 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#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(__(nil(),X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(__(X,nil())) -> mark#(X) 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#(U12(tt())) -> mark#(tt()) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(__(nil(),X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(__(X,nil())) -> mark#(X) 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#(U12(tt())) -> mark#(tt()) mark#(tt()) -> active#(tt()) -> active#(__(nil(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) -> active#(__(X,nil())) -> mark#(X) 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#(U12(tt())) -> mark#(tt()) mark#(nil()) -> active#(nil()) -> active#(__(nil(),X)) -> mark#(X) mark#(nil()) -> active#(nil()) -> active#(__(X,nil())) -> mark#(X) 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#(U12(tt())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(nil(),X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(X,nil())) -> mark#(X) 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#(U12(tt())) -> mark#(tt()) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(U12(tt())) -> mark#(tt()) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(U12(tt())) -> mark#(tt()) -> mark#(isNePal(X)) -> mark#(X) active#(U12(tt())) -> mark#(tt()) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(U12(tt())) -> mark#(tt()) -> mark#(U12(X)) -> U12#(mark(X)) active#(U12(tt())) -> mark#(tt()) -> mark#(U12(X)) -> mark#(X) active#(U12(tt())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(tt()) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(U12(tt())) -> mark#(tt()) -> mark#(U11(X)) -> U11#(mark(X)) active#(U12(tt())) -> mark#(tt()) -> mark#(U11(X)) -> mark#(X) active#(U12(tt())) -> mark#(tt()) -> mark#(nil()) -> active#(nil()) active#(U12(tt())) -> mark#(tt()) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U12(tt())) -> mark#(tt()) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(U12(tt())) -> mark#(tt()) -> mark#(__(X1,X2)) -> mark#(X1) active#(U12(tt())) -> mark#(tt()) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(nil(),X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(__(nil(),X)) -> mark#(X) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(__(nil(),X)) -> mark#(X) -> mark#(U12(X)) -> U12#(mark(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(__(nil(),X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(__(nil(),X)) -> mark#(X) -> mark#(U11(X)) -> U11#(mark(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(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) active#(__(X,nil())) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(__(X,nil())) -> mark#(X) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(__(X,nil())) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(__(X,nil())) -> mark#(X) -> mark#(U12(X)) -> U12#(mark(X)) active#(__(X,nil())) -> mark#(X) -> mark#(U12(X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(__(X,nil())) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(__(X,nil())) -> mark#(X) -> mark#(U11(X)) -> U11#(mark(X)) active#(__(X,nil())) -> mark#(X) -> mark#(U11(X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) SCC Processor: #sccs: 5 #rules: 25 #arcs: 217/961 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()) active#(__(X,nil())) -> mark#(X) mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) 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()) active#(__(X,nil())) -> mark#(X) mark#(U11(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(U12(tt())) -> mark#(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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) 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#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(X,nil())) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(nil(),X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(U12(tt())) -> mark#(tt()) 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#(U12(X)) -> active#(U12(mark(X))) -> active#(__(X,nil())) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(__(nil(),X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(U12(tt())) -> mark#(tt()) 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#(U11(X)) -> active#(U11(mark(X))) -> active#(__(X,nil())) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(__(nil(),X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(U12(tt())) -> mark#(tt()) 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))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(X,nil())) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(nil(),X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(U12(tt())) -> mark#(tt()) active#(U12(tt())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(nil(),X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(__(nil(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(__(nil(),X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(__(nil(),X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) 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))) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(__(X,nil())) -> mark#(X) -> mark#(U11(X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(__(X,nil())) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(__(X,nil())) -> mark#(X) -> mark#(U12(X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(__(X,nil())) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) SCC Processor: #sccs: 1 #rules: 12 #arcs: 103/225 DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(__(X,nil())) -> mark#(X) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) 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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) KBO Processor: 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 weight function: w0 = 1 w(mark#) = w(active#) = w(isNePal) = w(U12) = w(U11) = w(tt) = w( nil) = w(mark) = w(active) = w(__) = 1 precedence: isNePal > mark# ~ active# ~ 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#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) SCC Processor: #sccs: 1 #rules: 3 #arcs: 84/49 DPs: mark#(isNePal(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) 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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) 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))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Subterm Criterion Processor: simple projection: pi(__#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Qed DPs: U11#(mark(X)) -> U11#(X) U11#(active(X)) -> U11#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Subterm Criterion Processor: simple projection: pi(U11#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Qed DPs: U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Subterm Criterion Processor: simple projection: pi(U12#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Qed DPs: isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Subterm Criterion Processor: simple projection: pi(isNePal#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U12(tt())) -> mark(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) Qed