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: 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#(U11(tt())) -> U12#(tt()) active#(U11(tt())) -> mark#(U12(tt())) active#(U12(tt())) -> mark#(tt()) active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(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(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) 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#(U11(tt())) -> U12#(tt()) active#(U11(tt())) -> mark#(U12(tt())) active#(U12(tt())) -> mark#(tt()) active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(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(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) 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) 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) 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) 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#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(U12(tt())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(U11(tt())) -> mark#(U12(tt())) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(U11(tt())) -> U12#(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#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(U11(tt())) -> mark#(U12(tt())) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(U11(tt())) -> U12#(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#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(U12(tt())) -> mark#(tt()) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(U11(tt())) -> mark#(U12(tt())) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(U11(tt())) -> U12#(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#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(tt()) -> active#(tt()) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) mark#(tt()) -> active#(tt()) -> active#(U12(tt())) -> mark#(tt()) mark#(tt()) -> active#(tt()) -> active#(U11(tt())) -> mark#(U12(tt())) mark#(tt()) -> active#(tt()) -> active#(U11(tt())) -> U12#(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#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(nil()) -> active#(nil()) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) mark#(nil()) -> active#(nil()) -> active#(U12(tt())) -> mark#(tt()) mark#(nil()) -> active#(nil()) -> active#(U11(tt())) -> mark#(U12(tt())) mark#(nil()) -> active#(nil()) -> active#(U11(tt())) -> U12#(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#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(U12(tt())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(U11(tt())) -> mark#(U12(tt())) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(U11(tt())) -> U12#(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#(isNePal(__(I,__(P,I)))) -> U11#(tt()) -> U11#(active(X)) -> U11#(X) active#(isNePal(__(I,__(P,I)))) -> U11#(tt()) -> U11#(mark(X)) -> U11#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(isNePal(X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U12(X)) -> U12#(mark(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U12(X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(tt()) -> active#(tt()) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U11(X)) -> U11#(mark(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U11(X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(nil()) -> active#(nil()) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(__(X1,X2)) -> mark#(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#(U11(tt())) -> U12#(tt()) -> U12#(active(X)) -> U12#(X) active#(U11(tt())) -> U12#(tt()) -> U12#(mark(X)) -> U12#(X) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(isNePal(X)) -> mark#(X) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U12(X)) -> active#(U12(mark(X))) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U12(X)) -> U12#(mark(X)) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U12(X)) -> mark#(X) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(tt()) -> active#(tt()) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U11(X)) -> U11#(mark(X)) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U11(X)) -> mark#(X) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(nil()) -> active#(nil()) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(__(X1,X2)) -> mark#(X1) active#(U11(tt())) -> mark#(U12(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: 27 #arcs: 275/1225 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#(U11(tt())) -> mark#(U12(tt())) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U12(tt())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) 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())) 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#(U11(tt())) -> mark#(U12(tt())) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U12(tt())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) 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())) 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#(U11(tt())) -> mark#(U12(tt())) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(U12(tt())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(U11(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#(U11(tt())) -> mark#(U12(tt())) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(U12(tt())) -> mark#(tt()) mark#(U12(X)) -> active#(U12(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(U11(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#(U11(tt())) -> mark#(U12(tt())) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(U12(tt())) -> mark#(tt()) mark#(U11(X)) -> active#(U11(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(U11(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#(U11(tt())) -> mark#(U12(tt())) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(U12(tt())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U11(X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) -> mark#(U11(X)) -> active#(U11(mark(X))) active#(U12(tt())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U12(X)) -> mark#(X) active#(U11(tt())) -> mark#(U12(tt())) -> mark#(U12(X)) -> active#(U12(mark(X))) 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: 14 #arcs: 115/289 DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(U11(X)) -> active#(U11(mark(X))) active#(U11(tt())) -> mark#(U12(tt())) mark#(U12(X)) -> active#(U12(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) 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())) 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) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [isNePal](x0) = x0 + 0, [U12](x0) = x0 + 0, [U11](x0) = x0 + 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0 + 0, [__](x0, x1) = 1x0 + x1 + 0 orientation: mark#(isNePal(X)) = X + 0 >= X = mark#(X) mark#(isNePal(X)) = X + 0 >= X + 0 = active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) = 1I + 1P + 0 >= 0 = mark#(U11(tt())) mark#(U11(X)) = X + 0 >= X + 0 = active#(U11(mark(X))) active#(U11(tt())) = 0 >= 0 = mark#(U12(tt())) mark#(U12(X)) = X + 0 >= X + 0 = active#(U12(mark(X))) active#(__(nil(),X)) = X + 1 >= X = mark#(X) mark#(U12(X)) = X + 0 >= X = mark#(X) mark#(U11(X)) = X + 0 >= X = mark#(X) mark#(__(X1,X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = active#(__(mark(X1),mark(X2))) active#(__(X,nil())) = 1X + 0 >= X = mark#(X) mark#(__(X1,X2)) = 1X1 + X2 + 0 >= X1 = mark#(X1) mark#(__(X1,X2)) = 1X1 + X2 + 0 >= X2 = mark#(X2) active#(__(__(X,Y),Z)) = 2X + 1Y + Z + 1 >= 1X + 1Y + Z + 0 = mark#(__(X,__(Y,Z))) active(__(__(X,Y),Z)) = 2X + 1Y + Z + 1 >= 1X + 1Y + Z + 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1X + 0 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(U11(tt())) = 0 >= 0 = mark(U12(tt())) active(U12(tt())) = 0 >= 0 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 1I + 1P + 0 >= 0 = mark(U11(tt())) mark(__(X1,X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = X + 0 >= X + 0 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X + 0 >= X + 0 = active(U12(mark(X))) mark(isNePal(X)) = X + 0 >= X + 0 = active(isNePal(mark(X))) __(mark(X1),X2) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = __(X1,X2) __(X1,mark(X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = __(X1,X2) __(active(X1),X2) = 1X1 + X2 + 1 >= 1X1 + X2 + 0 = __(X1,X2) __(X1,active(X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = __(X1,X2) U11(mark(X)) = X + 0 >= X + 0 = U11(X) U11(active(X)) = X + 0 >= X + 0 = U11(X) U12(mark(X)) = X + 0 >= X + 0 = U12(X) U12(active(X)) = X + 0 >= X + 0 = U12(X) isNePal(mark(X)) = X + 0 >= X + 0 = isNePal(X) isNePal(active(X)) = X + 0 >= X + 0 = isNePal(X) problem: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(U11(tt())) mark#(U11(X)) -> active#(U11(mark(X))) active#(U11(tt())) -> mark#(U12(tt())) mark#(U12(X)) -> active#(U12(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) 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())) 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) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [isNePal](x0) = 2x0 + 0, [U12](x0) = x0 + 0, [U11](x0) = x0 + 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0 + 0, [__](x0, x1) = x0 + x1 + 0 orientation: mark#(isNePal(X)) = 2X + 0 >= X + 0 = mark#(X) mark#(isNePal(X)) = 2X + 0 >= 2X + 0 = active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) = 2I + 2P + 2 >= 0 = mark#(U11(tt())) mark#(U11(X)) = X + 0 >= X + 0 = active#(U11(mark(X))) active#(U11(tt())) = 0 >= 0 = mark#(U12(tt())) mark#(U12(X)) = X + 0 >= X + 0 = active#(U12(mark(X))) active#(__(nil(),X)) = X + 0 >= X + 0 = mark#(X) mark#(U12(X)) = X + 0 >= X + 0 = mark#(X) mark#(U11(X)) = X + 0 >= X + 0 = mark#(X) mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) active#(__(__(X,Y),Z)) = X + Y + Z + 0 >= X + Y + Z + 0 = mark#(__(X,__(Y,Z))) active(__(__(X,Y),Z)) = X + Y + Z + 0 >= X + Y + Z + 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 0 >= X = mark(X) active(__(nil(),X)) = X + 0 >= X = mark(X) active(U11(tt())) = 0 >= 0 = mark(U12(tt())) active(U12(tt())) = 0 >= 0 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 2I + 2P + 2 >= 0 = mark(U11(tt())) mark(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = X + 0 >= X + 0 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X + 0 >= X + 0 = active(U12(mark(X))) mark(isNePal(X)) = 2X + 0 >= 2X + 0 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) U11(mark(X)) = X + 0 >= X + 0 = U11(X) U11(active(X)) = X + 0 >= X + 0 = U11(X) U12(mark(X)) = X + 0 >= X + 0 = U12(X) U12(active(X)) = X + 0 >= X + 0 = U12(X) isNePal(mark(X)) = 2X + 0 >= 2X + 0 = isNePal(X) isNePal(active(X)) = 2X + 2 >= 2X + 0 = isNePal(X) problem: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U11(X)) -> active#(U11(mark(X))) active#(U11(tt())) -> mark#(U12(tt())) mark#(U12(X)) -> active#(U12(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) 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())) 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) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [isNePal](x0) = x0 + 0, [U12](x0) = x0 + 2, [U11](x0) = x0 + 7, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 0, [active](x0) = x0 + 0, [__](x0, x1) = x0 + x1 + 7 orientation: mark#(isNePal(X)) = X + 0 >= X + 0 = mark#(X) mark#(isNePal(X)) = X + 0 >= X + 0 = active#(isNePal(mark(X))) mark#(U11(X)) = X + 7 >= X + 7 = active#(U11(mark(X))) active#(U11(tt())) = 7 >= 2 = mark#(U12(tt())) mark#(U12(X)) = X + 2 >= X + 2 = active#(U12(mark(X))) active#(__(nil(),X)) = X + 7 >= X + 0 = mark#(X) mark#(U12(X)) = X + 2 >= X + 0 = mark#(X) mark#(U11(X)) = X + 7 >= X + 0 = mark#(X) mark#(__(X1,X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) = X1 + X2 + 7 >= X2 + 0 = mark#(X2) active#(__(__(X,Y),Z)) = X + Y + Z + 7 >= X + Y + Z + 7 = mark#(__(X,__(Y,Z))) active(__(__(X,Y),Z)) = X + Y + Z + 7 >= X + Y + Z + 7 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 7 >= X + 0 = mark(X) active(__(nil(),X)) = X + 7 >= X + 0 = mark(X) active(U11(tt())) = 7 >= 2 = mark(U12(tt())) active(U12(tt())) = 2 >= 0 = mark(tt()) active(isNePal(__(I,__(P,I)))) = I + P + 7 >= 7 = mark(U11(tt())) mark(__(X1,X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = X + 7 >= X + 7 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = X + 2 >= X + 2 = active(U12(mark(X))) mark(isNePal(X)) = X + 0 >= X + 0 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 + 7 >= X1 + X2 + 7 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 7 >= X1 + X2 + 7 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = __(X1,X2) U11(mark(X)) = X + 7 >= X + 7 = U11(X) U11(active(X)) = X + 7 >= X + 7 = U11(X) U12(mark(X)) = X + 2 >= X + 2 = U12(X) U12(active(X)) = X + 2 >= X + 2 = U12(X) isNePal(mark(X)) = X + 0 >= X + 0 = isNePal(X) isNePal(active(X)) = X + 0 >= X + 0 = isNePal(X) problem: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U11(X)) -> active#(U11(mark(X))) mark#(U12(X)) -> active#(U12(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(U12(X)) -> mark#(X) mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) 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())) 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) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [isNePal](x0) = 5x0 + 0, [U12](x0) = 5x0 + 1, [U11](x0) = 5x0 + 0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0 + 0, [__](x0, x1) = x0 + x1 + 0 orientation: mark#(isNePal(X)) = 5X + 0 >= X + 0 = mark#(X) mark#(isNePal(X)) = 5X + 0 >= 5X + 0 = active#(isNePal(mark(X))) mark#(U11(X)) = 5X + 0 >= 5X + 0 = active#(U11(mark(X))) mark#(U12(X)) = 5X + 1 >= 5X + 1 = active#(U12(mark(X))) active#(__(nil(),X)) = X + 0 >= X + 0 = mark#(X) mark#(U12(X)) = 5X + 1 >= X + 0 = mark#(X) mark#(U11(X)) = 5X + 0 >= X + 0 = mark#(X) mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) active#(__(__(X,Y),Z)) = X + Y + Z + 0 >= X + Y + Z + 0 = mark#(__(X,__(Y,Z))) active(__(__(X,Y),Z)) = X + Y + Z + 0 >= X + Y + Z + 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 0 >= X = mark(X) active(__(nil(),X)) = X + 0 >= X = mark(X) active(U11(tt())) = 5 >= 5 = mark(U12(tt())) active(U12(tt())) = 5 >= 0 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 5I + 5P + 5 >= 5 = mark(U11(tt())) mark(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = 5X + 0 >= 5X + 0 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X)) = 5X + 1 >= 5X + 1 = active(U12(mark(X))) mark(isNePal(X)) = 5X + 0 >= 5X + 0 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) U11(mark(X)) = 5X + 0 >= 5X + 0 = U11(X) U11(active(X)) = 5X + 5 >= 5X + 0 = U11(X) U12(mark(X)) = 5X + 1 >= 5X + 1 = U12(X) U12(active(X)) = 5X + 5 >= 5X + 1 = U12(X) isNePal(mark(X)) = 5X + 0 >= 5X + 0 = isNePal(X) isNePal(active(X)) = 5X + 5 >= 5X + 0 = isNePal(X) problem: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(U11(X)) -> active#(U11(mark(X))) mark#(U12(X)) -> active#(U12(mark(X))) active#(__(nil(),X)) -> mark#(X) mark#(U11(X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) 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())) 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(U11) = w(tt) = w(nil) = w( mark) = w(active) = w(__) = 1 w(U12) = 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#(U11(X)) -> active#(U11(mark(X))) mark#(U12(X)) -> active#(U12(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(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) SCC Processor: #sccs: 1 #rules: 2 #arcs: 96/36 DPs: mark#(isNePal(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(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) 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(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) 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(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) 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(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) 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())) 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(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) 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())) 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(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) 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())) 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(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) 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())) 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