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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U11(tt())) -> U12#(tt()) active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X)) -> active#(X) active#(U11(X)) -> U11#(active(X)) active#(U12(X)) -> active#(X) active#(U12(X)) -> U12#(active(X)) active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> isNePal#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X)) -> U11#(X) U12#(mark(X)) -> U12#(X) isNePal#(mark(X)) -> isNePal#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X)) -> proper#(X) proper#(U11(X)) -> U11#(proper(X)) proper#(U12(X)) -> proper#(X) proper#(U12(X)) -> U12#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X)) -> U11#(X) U12#(ok(X)) -> U12#(X) isNePal#(ok(X)) -> isNePal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U11(tt())) -> U12#(tt()) active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X)) -> active#(X) active#(U11(X)) -> U11#(active(X)) active#(U12(X)) -> active#(X) active#(U12(X)) -> U12#(active(X)) active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> isNePal#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X)) -> U11#(X) U12#(mark(X)) -> U12#(X) isNePal#(mark(X)) -> isNePal#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X)) -> proper#(X) proper#(U11(X)) -> U11#(proper(X)) proper#(U12(X)) -> proper#(X) proper#(U12(X)) -> U12#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X)) -> U11#(X) U12#(ok(X)) -> U12#(X) isNePal#(ok(X)) -> isNePal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) top#(ok(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(U12(X)) -> U12#(active(X)) top#(ok(X)) -> active#(X) -> active#(U12(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(U11(X)) -> U11#(active(X)) top#(ok(X)) -> active#(X) -> active#(U11(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) top#(ok(X)) -> active#(X) -> active#(U11(tt())) -> U12#(tt()) top#(ok(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) top#(ok(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(U12(X)) -> U12#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(U12(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(U11(X)) -> U11#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(U11(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isNePal(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(U12(X)) -> U12#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(U12(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(U11(X)) -> U11#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(U11(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isNePal(X)) -> isNePal#(proper(X)) -> isNePal#(ok(X)) -> isNePal#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) -> isNePal#(mark(X)) -> isNePal#(X) proper#(U12(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(U12(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(U12(X)) -> proper#(X) -> proper#(U12(X)) -> U12#(proper(X)) proper#(U12(X)) -> proper#(X) -> proper#(U12(X)) -> proper#(X) proper#(U12(X)) -> proper#(X) -> proper#(U11(X)) -> U11#(proper(X)) proper#(U12(X)) -> proper#(X) -> proper#(U11(X)) -> proper#(X) proper#(U12(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U12(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(U12(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(U12(X)) -> U12#(proper(X)) -> U12#(ok(X)) -> U12#(X) proper#(U12(X)) -> U12#(proper(X)) -> U12#(mark(X)) -> U12#(X) proper#(U11(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(U11(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(U11(X)) -> proper#(X) -> proper#(U12(X)) -> U12#(proper(X)) proper#(U11(X)) -> proper#(X) -> proper#(U12(X)) -> proper#(X) proper#(U11(X)) -> proper#(X) -> proper#(U11(X)) -> U11#(proper(X)) proper#(U11(X)) -> proper#(X) -> proper#(U11(X)) -> proper#(X) proper#(U11(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(U11(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(U11(X)) -> U11#(proper(X)) -> U11#(ok(X)) -> U11#(X) proper#(U11(X)) -> U11#(proper(X)) -> U11#(mark(X)) -> U11#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(U12(X)) -> U12#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(U12(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(U11(X)) -> U11#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(U11(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X1) -> proper#(U12(X)) -> U12#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(U12(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X1) -> proper#(U11(X)) -> U11#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(U11(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(mark(X1),X2) -> __#(X1,X2) isNePal#(ok(X)) -> isNePal#(X) -> isNePal#(ok(X)) -> isNePal#(X) isNePal#(ok(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(ok(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) U11#(ok(X)) -> U11#(X) -> U11#(ok(X)) -> U11#(X) U11#(ok(X)) -> U11#(X) -> U11#(mark(X)) -> U11#(X) U11#(mark(X)) -> U11#(X) -> U11#(ok(X)) -> U11#(X) U11#(mark(X)) -> U11#(X) -> U11#(mark(X)) -> U11#(X) U12#(ok(X)) -> U12#(X) -> U12#(ok(X)) -> U12#(X) U12#(ok(X)) -> U12#(X) -> U12#(mark(X)) -> U12#(X) U12#(mark(X)) -> U12#(X) -> U12#(ok(X)) -> U12#(X) U12#(mark(X)) -> U12#(X) -> U12#(mark(X)) -> U12#(X) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) -> U11#(ok(X)) -> U11#(X) active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) -> U11#(mark(X)) -> U11#(X) active#(isNePal(X)) -> isNePal#(active(X)) -> isNePal#(ok(X)) -> isNePal#(X) active#(isNePal(X)) -> isNePal#(active(X)) -> isNePal#(mark(X)) -> isNePal#(X) active#(isNePal(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(isNePal(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> active#(X) -> active#(U12(X)) -> U12#(active(X)) active#(isNePal(X)) -> active#(X) -> active#(U12(X)) -> active#(X) active#(isNePal(X)) -> active#(X) -> active#(U11(X)) -> U11#(active(X)) active#(isNePal(X)) -> active#(X) -> active#(U11(X)) -> active#(X) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) active#(isNePal(X)) -> active#(X) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(isNePal(X)) -> active#(X) -> active#(U11(tt())) -> U12#(tt()) active#(isNePal(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(isNePal(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(U12(X)) -> U12#(active(X)) -> U12#(ok(X)) -> U12#(X) active#(U12(X)) -> U12#(active(X)) -> U12#(mark(X)) -> U12#(X) active#(U12(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(U12(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) active#(U12(X)) -> active#(X) -> active#(U12(X)) -> U12#(active(X)) active#(U12(X)) -> active#(X) -> active#(U12(X)) -> active#(X) active#(U12(X)) -> active#(X) -> active#(U11(X)) -> U11#(active(X)) active#(U12(X)) -> active#(X) -> active#(U11(X)) -> active#(X) active#(U12(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U12(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) active#(U12(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(U12(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) active#(U12(X)) -> active#(X) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(U12(X)) -> active#(X) -> active#(U11(tt())) -> U12#(tt()) active#(U12(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U12(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(U11(tt())) -> U12#(tt()) -> U12#(ok(X)) -> U12#(X) active#(U11(tt())) -> U12#(tt()) -> U12#(mark(X)) -> U12#(X) active#(U11(X)) -> U11#(active(X)) -> U11#(ok(X)) -> U11#(X) active#(U11(X)) -> U11#(active(X)) -> U11#(mark(X)) -> U11#(X) active#(U11(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(U11(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) active#(U11(X)) -> active#(X) -> active#(U12(X)) -> U12#(active(X)) active#(U11(X)) -> active#(X) -> active#(U12(X)) -> active#(X) active#(U11(X)) -> active#(X) -> active#(U11(X)) -> U11#(active(X)) active#(U11(X)) -> active#(X) -> active#(U11(X)) -> active#(X) active#(U11(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) active#(U11(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(U11(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) active#(U11(X)) -> active#(X) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(U11(X)) -> active#(X) -> active#(U11(tt())) -> U12#(tt()) active#(U11(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U11(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(ok(X1),ok(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)) -> __#(ok(X1),ok(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#(__(X1,X2)) -> __#(active(X1),X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(active(X1),X2) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(active(X1),X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(X)) -> active#(X) active#(__(X1,X2)) -> active#(X2) -> active#(U12(X)) -> U12#(active(X)) active#(__(X1,X2)) -> active#(X2) -> active#(U12(X)) -> active#(X) active#(__(X1,X2)) -> active#(X2) -> active#(U11(X)) -> U11#(active(X)) active#(__(X1,X2)) -> active#(X2) -> active#(U11(X)) -> active#(X) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(__(X1,X2)) -> active#(X2) -> active#(U11(tt())) -> U12#(tt()) active#(__(X1,X2)) -> active#(X2) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X2) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> active#(X) active#(__(X1,X2)) -> active#(X1) -> active#(U12(X)) -> U12#(active(X)) active#(__(X1,X2)) -> active#(X1) -> active#(U12(X)) -> active#(X) active#(__(X1,X2)) -> active#(X1) -> active#(U11(X)) -> U11#(active(X)) active#(__(X1,X2)) -> active#(X1) -> active#(U11(X)) -> active#(X) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(__(X1,X2)) -> active#(X1) -> active#(U11(tt())) -> U12#(tt()) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) SCC Processor: #sccs: 7 #rules: 21 #arcs: 198/1296 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) LPO 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(proper) = 0 pi(ok) = 0 pi(top) = 0 pi(top#) = 0 precedence: isNePal > U11 > U12 > __ > top# ~ top ~ ok ~ proper ~ tt ~ nil ~ mark ~ active problem: DPs: top#(ok(X)) -> top#(active(X)) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) KBO Processor: argument filtering: pi(__) = [0] pi(active) = 0 pi(mark) = [] pi(nil) = [] pi(tt) = [] pi(U11) = 0 pi(U12) = 0 pi(isNePal) = 0 pi(proper) = [0] pi(ok) = [0] pi(top) = [] pi(top#) = 0 weight function: w0 = 1 w(top#) = w(top) = w(ok) = w(proper) = w(tt) = w(nil) = w(mark) = w( __) = 1 w(isNePal) = w(U12) = w(U11) = w(active) = 0 precedence: proper > __ > tt > top# ~ top ~ ok ~ isNePal ~ U12 ~ U11 ~ nil ~ mark ~ active problem: DPs: TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) active#(U11(X)) -> active#(X) active#(U12(X)) -> active#(X) active#(isNePal(X)) -> active#(X) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(active#) = 0 problem: DPs: TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(U11(X)) -> proper#(X) proper#(U12(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(proper#) = 0 problem: DPs: TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNePal#(mark(X)) -> isNePal#(X) isNePal#(ok(X)) -> isNePal#(X) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(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(U11(tt())) -> mark(U12(tt())) active(U12(tt())) -> mark(tt()) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U12#(mark(X)) -> U12#(X) U12#(ok(X)) -> U12#(X) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(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(U11(tt())) -> mark(U12(tt())) active(U12(tt())) -> mark(tt()) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U11#(mark(X)) -> U11#(X) U11#(ok(X)) -> U11#(X) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(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(U11(tt())) -> mark(U12(tt())) active(U12(tt())) -> mark(tt()) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(__#) = 1 problem: DPs: __#(mark(X1),X2) -> __#(X1,X2) TRS: 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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(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(U11(tt())) -> mark(U12(tt())) active(U12(tt())) -> mark(tt()) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed