MAYBE Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) 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#(and(tt(),X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) 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) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) 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(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) 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#(and(tt(),X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) 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) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) 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(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) 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) and#(mark(X1),X2) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) 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#(tt()) -> active#(tt()) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) 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#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(and(tt(),X)) -> mark#(X) 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#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(X1,active(X2)) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(active(X1),X2) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(X1,mark(X2)) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(mark(X1),X2) -> and#(X1,X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(and(tt(),X)) -> mark#(X) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(nil(),X)) -> mark#(X) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(X,nil())) -> mark#(X) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(tt()) -> active#(tt()) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(tt()) -> active#(tt()) -> active#(and(tt(),X)) -> mark#(X) 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#(tt()) mark#(nil()) -> active#(nil()) -> active#(and(tt(),X)) -> mark#(X) 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#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) 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#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) 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#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(and(tt(),X)) -> mark#(X) 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)))) -> mark#(tt()) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(isNePal(X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(nil()) -> active#(nil()) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(and(tt(),X)) -> mark#(X) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) active#(and(tt(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(and(tt(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> 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#(tt()) -> active#(tt()) active#(__(nil(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(nil(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(__(nil(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) 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#(tt()) -> active#(tt()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> mark#(X1) 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#(tt()) -> active#(tt()) active#(__(X,nil())) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(X,nil())) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(__(X,nil())) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) 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: 4 #rules: 24 #arcs: 197/841 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#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(nil(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [active#](x0) = x0 + 1, [isNePal](x0) = x0 + 1, [and](x0, x1) = x0 + x1 + 1, [tt] = 1, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: mark#(isNePal(X)) = X + 2 >= X + 1 = mark#(X) mark#(__(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = mark#(X2) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark#(__(X,__(Y,Z))) mark#(nil()) = 2 >= 2 = active#(nil()) active#(__(X,nil())) = X + 2 >= X + 1 = mark#(X) mark#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = active#(and(mark(X1),X2)) active#(__(nil(),X)) = X + 2 >= X + 1 = mark#(X) mark#(tt()) = 2 >= 2 = active#(tt()) active#(and(tt(),X)) = X + 3 >= X + 1 = mark#(X) mark#(isNePal(X)) = X + 2 >= X + 2 = active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 2 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X = mark(X) active(__(nil(),X)) = X + 1 >= X = mark(X) active(and(tt(),X)) = X + 2 >= X = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 1 = mark(tt()) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(and(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(isNePal(X)) = X + 1 >= X + 1 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) and(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) and(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) isNePal(mark(X)) = X + 1 >= X + 1 = isNePal(X) isNePal(active(X)) = X + 1 >= X + 1 = isNePal(X) problem: DPs: mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [active#](x0) = x0 + 1, [isNePal](x0) = 0, [and](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: mark#(__(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = mark#(X2) mark#(__(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark#(__(X,__(Y,Z))) mark#(nil()) = 2 >= 2 = active#(nil()) mark#(and(X1,X2)) = X2 + 1 >= X2 + 1 = active#(and(mark(X1),X2)) mark#(tt()) = 1 >= 1 = active#(tt()) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark#(tt()) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X = mark(X) active(__(nil(),X)) = X + 2 >= X = mark(X) active(and(tt(),X)) = X >= X = mark(X) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(and(X1,X2)) = X2 >= X2 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(isNePal(X)) = 0 >= 0 = active(isNePal(mark(X))) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2) and(mark(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,mark(X2)) = X2 >= X2 = and(X1,X2) and(active(X1),X2) = X2 >= X2 = and(X1,X2) and(X1,active(X2)) = X2 >= X2 = and(X1,X2) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) problem: DPs: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [isNePal](x0) = 1, [and](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = 1 orientation: mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(nil()) = 0 >= 0 = active#(nil()) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(tt()) = 0 >= 0 = active#(tt()) mark#(isNePal(X)) = 1 >= 1 = active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) = 1 >= 0 = mark#(tt()) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(tt()) mark(__(X1,X2)) = 1 >= 1 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 0 = active(nil()) mark(and(X1,X2)) = 1 >= 1 = active(and(mark(X1),X2)) mark(tt()) = 1 >= 0 = active(tt()) mark(isNePal(X)) = 1 >= 1 = active(isNePal(mark(X))) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isNePal(mark(X)) = 1 >= 1 = isNePal(X) isNePal(active(X)) = 1 >= 1 = isNePal(X) problem: DPs: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [isNePal](x0) = 0, [and](x0, x1) = 1, [tt] = 1, [nil] = 1, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 1 orientation: mark#(__(X1,X2)) = 1 >= 1 = active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) = 1 >= 1 = mark#(__(X,__(Y,Z))) mark#(nil()) = 1 >= 1 = active#(nil()) mark#(and(X1,X2)) = 1 >= 1 = active#(and(mark(X1),X2)) mark#(tt()) = 1 >= 1 = active#(tt()) mark#(isNePal(X)) = 1 >= 0 = active#(isNePal(mark(X))) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(isNePal(X)) = 0 >= 0 = active(isNePal(mark(X))) __(mark(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,mark(X2)) = 1 >= 1 = __(X1,X2) __(active(X1),X2) = 1 >= 1 = __(X1,X2) __(X1,active(X2)) = 1 >= 1 = __(X1,X2) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) problem: DPs: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [isNePal](x0) = 0, [and](x0, x1) = 0, [tt] = 1, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 0 orientation: mark#(__(X1,X2)) = 0 >= 0 = active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) = 0 >= 0 = mark#(__(X,__(Y,Z))) mark#(nil()) = 0 >= 0 = active#(nil()) mark#(and(X1,X2)) = 0 >= 0 = active#(and(mark(X1),X2)) mark#(tt()) = 1 >= 0 = active#(tt()) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(isNePal(X)) = 0 >= 0 = active(isNePal(mark(X))) __(mark(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,mark(X2)) = 0 >= 0 = __(X1,X2) __(active(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,active(X2)) = 0 >= 0 = __(X1,X2) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) problem: DPs: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [isNePal](x0) = 0, [and](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 0 orientation: mark#(__(X1,X2)) = 0 >= 0 = active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) = 0 >= 0 = mark#(__(X,__(Y,Z))) mark#(nil()) = 0 >= 0 = active#(nil()) mark#(and(X1,X2)) = 1 >= 0 = active#(and(mark(X1),X2)) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(isNePal(X)) = 0 >= 0 = active(isNePal(mark(X))) __(mark(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,mark(X2)) = 0 >= 0 = __(X1,X2) __(active(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,active(X2)) = 0 >= 0 = __(X1,X2) and(mark(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,mark(X2)) = 1 >= 1 = and(X1,X2) and(active(X1),X2) = 1 >= 1 = and(X1,X2) and(X1,active(X2)) = 1 >= 1 = and(X1,X2) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) problem: DPs: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [isNePal](x0) = 0, [and](x0, x1) = 0, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 0 orientation: mark#(__(X1,X2)) = 0 >= 0 = active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) = 0 >= 0 = mark#(__(X,__(Y,Z))) mark#(nil()) = 1 >= 0 = active#(nil()) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(tt()) mark(__(X1,X2)) = 0 >= 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(and(X1,X2)) = 0 >= 0 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(isNePal(X)) = 0 >= 0 = active(isNePal(mark(X))) __(mark(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,mark(X2)) = 0 >= 0 = __(X1,X2) __(active(X1),X2) = 0 >= 0 = __(X1,X2) __(X1,active(X2)) = 0 >= 0 = __(X1,X2) and(mark(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,mark(X2)) = 0 >= 0 = and(X1,X2) and(active(X1),X2) = 0 >= 0 = and(X1,X2) and(X1,active(X2)) = 0 >= 0 = and(X1,X2) isNePal(mark(X)) = 0 >= 0 = isNePal(X) isNePal(active(X)) = 0 >= 0 = isNePal(X) problem: DPs: mark#(__(X1,X2)) -> active#(__(mark(X1),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(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Open 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(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Open DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Open 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(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) 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) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Open