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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(and(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> and#(active(X1),X2) active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> isNePal#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) isNePal#(mark(X)) -> isNePal#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) isNePal#(ok(X)) -> isNePal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(and(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> and#(active(X1),X2) active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> isNePal#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) isNePal#(mark(X)) -> isNePal#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) isNePal#(ok(X)) -> isNePal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) top#(ok(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(and(X1,X2)) -> and#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) top#(ok(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isNePal(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) proper#(isNePal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isNePal(X)) -> isNePal#(proper(X)) -> isNePal#(ok(X)) -> isNePal#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) -> isNePal#(mark(X)) -> isNePal#(X) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) -> and#(mark(X1),X2) -> and#(X1,X2) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(mark(X1),X2) -> __#(X1,X2) isNePal#(ok(X)) -> isNePal#(X) -> isNePal#(ok(X)) -> isNePal#(X) isNePal#(ok(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(ok(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) and#(ok(X1),ok(X2)) -> and#(X1,X2) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(isNePal(X)) -> isNePal#(active(X)) -> isNePal#(ok(X)) -> isNePal#(X) active#(isNePal(X)) -> isNePal#(active(X)) -> isNePal#(mark(X)) -> isNePal#(X) active#(isNePal(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(isNePal(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> active#(X) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(isNePal(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) active#(isNePal(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(isNePal(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(and(X1,X2)) -> and#(active(X1),X2) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) active#(and(X1,X2)) -> and#(active(X1),X2) -> and#(mark(X1),X2) -> and#(X1,X2) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> active#(X) active#(and(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(and(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X2) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(and(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(X1,X2)) -> __#(active(X1),X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(active(X1),X2) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(active(X1),X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(X)) -> active#(X) active#(__(X1,X2)) -> active#(X2) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) -> active#(and(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X2) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> active#(X) active#(__(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(__(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) EDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(and(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> and#(active(X1),X2) active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> isNePal#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) isNePal#(mark(X)) -> isNePal#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) isNePal#(ok(X)) -> isNePal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) top#(ok(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(and(X1,X2)) -> and#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(isNePal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) proper#(isNePal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) proper#(isNePal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isNePal(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isNePal(X)) -> isNePal#(proper(X)) -> isNePal#(mark(X)) -> isNePal#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) -> isNePal#(ok(X)) -> isNePal#(X) proper#(and(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) -> and#(mark(X1),X2) -> and#(X1,X2) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X2) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X2) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X1) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(X1) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(mark(X1),X2) -> __#(X1,X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) isNePal#(ok(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) isNePal#(ok(X)) -> isNePal#(X) -> isNePal#(ok(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(ok(X)) -> isNePal#(X) and#(ok(X1),ok(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(isNePal(X)) -> isNePal#(active(X)) -> isNePal#(mark(X)) -> isNePal#(X) active#(isNePal(X)) -> isNePal#(active(X)) -> isNePal#(ok(X)) -> isNePal#(X) active#(isNePal(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(isNePal(X)) -> active#(X) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X1) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> active#(X2) active#(isNePal(X)) -> active#(X) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(isNePal(X)) -> active#(X) -> active#(and(X1,X2)) -> active#(X1) active#(isNePal(X)) -> active#(X) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(isNePal(X)) -> active#(X) -> active#(isNePal(X)) -> active#(X) active#(isNePal(X)) -> active#(X) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(and(X1,X2)) -> and#(active(X1),X2) -> and#(mark(X1),X2) -> and#(X1,X2) active#(and(X1,X2)) -> and#(active(X1),X2) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) active#(and(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(and(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X2) active#(and(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(and(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> active#(X) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(active(X1),X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(X1,X2)) -> __#(active(X1),X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> __#(X1,active(X2)) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) active#(__(X1,X2)) -> active#(X2) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(X1,X2)) -> active#(X2) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X2) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(__(X1,X2)) -> active#(X2) -> active#(and(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(X)) -> active#(X) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(X)) -> isNePal#(active(X)) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X1) -> active#(__(X1,X2)) -> __#(X1,active(X2)) active#(__(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X1) -> active#(and(X1,X2)) -> and#(active(X1),X2) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> active#(X) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(X)) -> isNePal#(active(X)) SCC Processor: #sccs: 6 #rules: 18 #arcs: 141/841 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: proper#(isNePal(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [isNePal](x0) = x0 + 1, [and](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: proper#(isNePal(X)) = X + 2 >= X + 1 = proper#(X) proper#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(and(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(__(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = proper#(X1) proper#(__(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = proper#(X2) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= 0 = mark(X) active(__(nil(),X)) = X + 2 >= 0 = mark(X) active(and(tt(),X)) = X + 2 >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = and(active(X1),X2) active(isNePal(X)) = X + 2 >= X + 2 = isNePal(active(X)) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 + 1 >= 0 = mark(and(X1,X2)) isNePal(mark(X)) = 1 >= 0 = mark(isNePal(X)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(and(X1,X2)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> proper#(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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [isNePal](x0) = x0, [and](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: proper#(__(X1,X2)) = X1 + X2 + 1 >= X1 = proper#(X1) proper#(__(X1,X2)) = X1 + X2 + 1 >= X2 = proper#(X2) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= 1 = mark(X) active(__(nil(),X)) = X + 1 >= 1 = mark(X) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = 1 >= 1 = and(active(X1),X2) active(isNePal(X)) = X >= X = isNePal(active(X)) __(mark(X1),X2) = X2 + 2 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 2 >= 1 = mark(__(X1,X2)) and(mark(X1),X2) = 1 >= 1 = mark(and(X1,X2)) isNePal(mark(X)) = 1 >= 1 = mark(isNePal(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = 1 >= 1 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = X >= X = isNePal(proper(X)) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 1 >= 1 = ok(and(X1,X2)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: 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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: active#(isNePal(X)) -> active#(X) active#(and(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X1) 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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [isNePal](x0) = x0 + 1, [and](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: active#(isNePal(X)) = X + 2 >= X + 1 = active#(X) active#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(__(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = active#(X2) active#(__(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= 0 = mark(X) active(__(nil(),X)) = X + 1 >= 0 = mark(X) active(and(tt(),X)) = X + 2 >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = and(active(X1),X2) active(isNePal(X)) = X + 2 >= X + 2 = isNePal(active(X)) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 + 1 >= 0 = mark(and(X1,X2)) isNePal(mark(X)) = 1 >= 0 = mark(isNePal(X)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) __(ok(X1),ok(X2)) = 0 >= 0 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 1 >= 0 = ok(and(X1,X2)) isNePal(ok(X)) = 1 >= 0 = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> active#(X1) 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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [isNePal](x0) = 0, [and](x0, x1) = 0, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(X1,X2)) = X1 + X2 + 1 >= X2 = active#(X2) active#(__(X1,X2)) = X1 + X2 + 1 >= X1 = active#(X1) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= 0 = mark(X) active(__(nil(),X)) = X + 2 >= 0 = mark(X) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = 0 >= 0 = and(active(X1),X2) active(isNePal(X)) = 0 >= 0 = isNePal(active(X)) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) isNePal(mark(X)) = 0 >= 0 = mark(isNePal(X)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 0 >= 0 = ok(and(X1,X2)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: 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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [isNePal](x0) = x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: __#(ok(X1),ok(X2)) = X1 >= X1 = __#(X1,X2) __#(X1,mark(X2)) = X1 >= X1 = __#(X1,X2) __#(mark(X1),X2) = X1 + 1 >= X1 = __#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) active(isNePal(X)) = X + 1 >= X + 1 = isNePal(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) isNePal(mark(X)) = X + 1 >= X + 1 = mark(isNePal(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [isNePal](x0) = x0, [and](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: __#(ok(X1),ok(X2)) = X1 + 1 >= X1 = __#(X1,X2) __#(X1,mark(X2)) = X1 >= X1 = __#(X1,X2) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(and(tt(),X)) = X >= 0 = mark(X) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) active(isNePal(X)) = X >= X = isNePal(active(X)) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) isNePal(mark(X)) = 0 >= 0 = mark(isNePal(X)) proper(__(X1,X2)) = 1 >= 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(and(X1,X2)) = 1 >= 1 = and(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: __#(X1,mark(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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x1, [top](x0) = 1, [ok](x0) = 0, [proper](x0) = x0, [isNePal](x0) = x0, [and](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: __#(X1,mark(X2)) = X2 + 1 >= X2 = __#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(and(tt(),X)) = X + 2 >= X + 1 = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = and(active(X1),X2) active(isNePal(X)) = X + 1 >= X + 1 = isNePal(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(and(X1,X2)) isNePal(mark(X)) = X + 1 >= X + 1 = mark(isNePal(X)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = X >= X = isNePal(proper(X)) __(ok(X1),ok(X2)) = 0 >= 0 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 1 >= 0 = ok(and(X1,X2)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: 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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: and#(ok(X1),ok(X2)) -> and#(X1,X2) and#(mark(X1),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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [and#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [isNePal](x0) = x0, [and](x0, x1) = x0, [tt] = 1, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: and#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = and#(X1,X2) and#(mark(X1),X2) = X2 + 1 >= X2 + 1 = and#(X1,X2) active(__(__(X,Y),Z)) = Z + 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = X + 1 >= 1 = mark(X) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isNePal(__(I,__(P,I)))) = I + 2 >= 1 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) active(isNePal(X)) = X >= X = isNePal(active(X)) __(mark(X1),X2) = X2 + 1 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = 2 >= 1 = mark(__(X1,X2)) and(mark(X1),X2) = 1 >= 1 = mark(and(X1,X2)) isNePal(mark(X)) = 1 >= 1 = mark(isNePal(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(tt()) = 2 >= 2 = ok(tt()) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: and#(mark(X1),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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [and#](x0, x1) = x0, [top](x0) = 1, [ok](x0) = 0, [proper](x0) = x0, [isNePal](x0) = x0, [and](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: and#(mark(X1),X2) = X1 + 1 >= X1 = and#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(and(tt(),X)) = X + 2 >= X + 1 = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = and(active(X1),X2) active(isNePal(X)) = X + 1 >= X + 1 = isNePal(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(and(X1,X2)) isNePal(mark(X)) = X + 1 >= X + 1 = mark(isNePal(X)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = X >= X = isNePal(proper(X)) __(ok(X1),ok(X2)) = 0 >= 0 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 1 >= 0 = ok(and(X1,X2)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: 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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNePal#(ok(X)) -> isNePal#(X) isNePal#(mark(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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isNePal#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [isNePal](x0) = x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: isNePal#(ok(X)) = X >= X = isNePal#(X) isNePal#(mark(X)) = X + 1 >= X = isNePal#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) active(isNePal(X)) = X + 1 >= X + 1 = isNePal(active(X)) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) isNePal(mark(X)) = X + 1 >= X + 1 = mark(isNePal(X)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: isNePal#(ok(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isNePal#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [isNePal](x0) = x0, [and](x0, x1) = x0, [tt] = 1, [nil] = 1, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = x1 + 1 orientation: isNePal#(ok(X)) = X + 2 >= X + 1 = isNePal#(X) active(__(__(X,Y),Z)) = Z + 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 2 >= 1 = mark(X) active(__(nil(),X)) = X + 1 >= 1 = mark(X) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isNePal(__(I,__(P,I)))) = I + 2 >= 1 = mark(tt()) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) active(isNePal(X)) = X >= X = isNePal(active(X)) __(mark(X1),X2) = X2 + 1 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = 2 >= 1 = mark(__(X1,X2)) and(mark(X1),X2) = 1 >= 1 = mark(and(X1,X2)) isNePal(mark(X)) = 1 >= 1 = mark(isNePal(X)) proper(__(X1,X2)) = X2 + 2 >= X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(tt()) = 2 >= 2 = ok(tt()) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: 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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed