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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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#(isList(V)) -> isNeList#(V) active#(isList(__(V1,V2))) -> isList#(V2) active#(isList(__(V1,V2))) -> isList#(V1) active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) active#(isNeList(V)) -> isQid#(V) active#(isNeList(__(V1,V2))) -> isNeList#(V2) active#(isNeList(__(V1,V2))) -> isList#(V1) active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) active#(isNeList(__(V1,V2))) -> isList#(V2) active#(isNeList(__(V1,V2))) -> isNeList#(V1) active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) active#(isNePal(V)) -> isQid#(V) active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) active#(isPal(V)) -> isNePal#(V) 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) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) 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#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) isList#(ok(X)) -> isList#(X) isNeList#(ok(X)) -> isNeList#(X) isQid#(ok(X)) -> isQid#(X) isNePal#(ok(X)) -> isNePal#(X) isPal#(ok(X)) -> isPal#(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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#(isList(V)) -> isNeList#(V) active#(isList(__(V1,V2))) -> isList#(V2) active#(isList(__(V1,V2))) -> isList#(V1) active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) active#(isNeList(V)) -> isQid#(V) active#(isNeList(__(V1,V2))) -> isNeList#(V2) active#(isNeList(__(V1,V2))) -> isList#(V1) active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) active#(isNeList(__(V1,V2))) -> isList#(V2) active#(isNeList(__(V1,V2))) -> isNeList#(V1) active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) active#(isNePal(V)) -> isQid#(V) active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) active#(isPal(V)) -> isNePal#(V) 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) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) 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#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) isList#(ok(X)) -> isList#(X) isNeList#(ok(X)) -> isNeList#(X) isQid#(ok(X)) -> isQid#(X) isNePal#(ok(X)) -> isNePal#(X) isPal#(ok(X)) -> isPal#(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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#(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#(isPal(V)) -> isNePal#(V) top#(ok(X)) -> active#(X) -> active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) top#(ok(X)) -> active#(X) -> active#(isNePal(__(I,__(P,I)))) -> isQid#(I) top#(ok(X)) -> active#(X) -> active#(isNePal(__(I,__(P,I)))) -> isPal#(P) top#(ok(X)) -> active#(X) -> active#(isNePal(V)) -> isQid#(V) top#(ok(X)) -> active#(X) -> active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) top#(ok(X)) -> active#(X) -> active#(isNeList(__(V1,V2))) -> isNeList#(V1) top#(ok(X)) -> active#(X) -> active#(isNeList(__(V1,V2))) -> isList#(V2) top#(ok(X)) -> active#(X) -> active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) top#(ok(X)) -> active#(X) -> active#(isNeList(__(V1,V2))) -> isList#(V1) top#(ok(X)) -> active#(X) -> active#(isNeList(__(V1,V2))) -> isNeList#(V2) top#(ok(X)) -> active#(X) -> active#(isNeList(V)) -> isQid#(V) top#(ok(X)) -> active#(X) -> active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) top#(ok(X)) -> active#(X) -> active#(isList(__(V1,V2))) -> isList#(V1) top#(ok(X)) -> active#(X) -> active#(isList(__(V1,V2))) -> isList#(V2) top#(ok(X)) -> active#(X) -> active#(isList(V)) -> isNeList#(V) 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#(isPal(X)) -> isPal#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(isPal(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#(isQid(X)) -> isQid#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(isQid(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(isNeList(X)) -> isNeList#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(isNeList(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(isList(X)) -> isList#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(isList(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#(isPal(X)) -> proper#(X) -> proper#(isPal(X)) -> isPal#(proper(X)) proper#(isPal(X)) -> proper#(X) -> proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isPal(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) -> proper#(isQid(X)) -> isQid#(proper(X)) proper#(isPal(X)) -> proper#(X) -> proper#(isQid(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(isPal(X)) -> proper#(X) -> proper#(isNeList(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) -> proper#(isList(X)) -> isList#(proper(X)) proper#(isPal(X)) -> proper#(X) -> proper#(isList(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isPal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) proper#(isPal(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) proper#(isPal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(isPal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(isPal(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isPal(X)) -> isPal#(proper(X)) -> isPal#(ok(X)) -> isPal#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(isPal(X)) -> isPal#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(isPal(X)) -> proper#(X) 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#(isQid(X)) -> isQid#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(isQid(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(isNeList(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) -> proper#(isList(X)) -> isList#(proper(X)) proper#(isNePal(X)) -> proper#(X) -> proper#(isList(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#(isQid(X)) -> proper#(X) -> proper#(isPal(X)) -> isPal#(proper(X)) proper#(isQid(X)) -> proper#(X) -> proper#(isPal(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isQid(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) -> proper#(isQid(X)) -> isQid#(proper(X)) proper#(isQid(X)) -> proper#(X) -> proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(isQid(X)) -> proper#(X) -> proper#(isNeList(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) -> proper#(isList(X)) -> isList#(proper(X)) proper#(isQid(X)) -> proper#(X) -> proper#(isList(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isQid(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) proper#(isQid(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) proper#(isQid(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(isQid(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(isQid(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isQid(X)) -> isQid#(proper(X)) -> isQid#(ok(X)) -> isQid#(X) proper#(isNeList(X)) -> proper#(X) -> proper#(isPal(X)) -> isPal#(proper(X)) proper#(isNeList(X)) -> proper#(X) -> proper#(isPal(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isNeList(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) -> proper#(isQid(X)) -> isQid#(proper(X)) proper#(isNeList(X)) -> proper#(X) -> proper#(isQid(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(isNeList(X)) -> proper#(X) -> proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) -> proper#(isList(X)) -> isList#(proper(X)) proper#(isNeList(X)) -> proper#(X) -> proper#(isList(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isNeList(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) proper#(isNeList(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) proper#(isNeList(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(isNeList(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(isNeList(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isNeList(X)) -> isNeList#(proper(X)) -> isNeList#(ok(X)) -> isNeList#(X) proper#(isList(X)) -> proper#(X) -> proper#(isPal(X)) -> isPal#(proper(X)) proper#(isList(X)) -> proper#(X) -> proper#(isPal(X)) -> proper#(X) proper#(isList(X)) -> proper#(X) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(isList(X)) -> proper#(X) -> proper#(isNePal(X)) -> proper#(X) proper#(isList(X)) -> proper#(X) -> proper#(isQid(X)) -> isQid#(proper(X)) proper#(isList(X)) -> proper#(X) -> proper#(isQid(X)) -> proper#(X) proper#(isList(X)) -> proper#(X) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(isList(X)) -> proper#(X) -> proper#(isNeList(X)) -> proper#(X) proper#(isList(X)) -> proper#(X) -> proper#(isList(X)) -> isList#(proper(X)) proper#(isList(X)) -> proper#(X) -> proper#(isList(X)) -> proper#(X) proper#(isList(X)) -> proper#(X) -> proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isList(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X1) proper#(isList(X)) -> proper#(X) -> proper#(and(X1,X2)) -> proper#(X2) proper#(isList(X)) -> proper#(X) -> proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(isList(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X1) proper#(isList(X)) -> proper#(X) -> proper#(__(X1,X2)) -> proper#(X2) proper#(isList(X)) -> isList#(proper(X)) -> isList#(ok(X)) -> isList#(X) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isPal(X)) -> isPal#(proper(X)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isPal(X)) -> proper#(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#(isQid(X)) -> isQid#(proper(X)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isQid(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isNeList(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isList(X)) -> isList#(proper(X)) proper#(and(X1,X2)) -> proper#(X2) -> proper#(isList(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#(isPal(X)) -> isPal#(proper(X)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isPal(X)) -> proper#(X) 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#(isQid(X)) -> isQid#(proper(X)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isQid(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isNeList(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isList(X)) -> isList#(proper(X)) proper#(and(X1,X2)) -> proper#(X1) -> proper#(isList(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#(isPal(X)) -> isPal#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isPal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNePal(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isQid(X)) -> isQid#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isQid(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isNeList(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isList(X)) -> isList#(proper(X)) proper#(__(X1,X2)) -> proper#(X2) -> proper#(isList(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#(isPal(X)) -> isPal#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isPal(X)) -> proper#(X) 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#(isQid(X)) -> isQid#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isQid(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isNeList(X)) -> proper#(X) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isList(X)) -> isList#(proper(X)) proper#(__(X1,X2)) -> proper#(X1) -> proper#(isList(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) isPal#(ok(X)) -> isPal#(X) -> isPal#(ok(X)) -> isPal#(X) isQid#(ok(X)) -> isQid#(X) -> isQid#(ok(X)) -> isQid#(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) isList#(ok(X)) -> isList#(X) -> isList#(ok(X)) -> isList#(X) isNeList#(ok(X)) -> isNeList#(X) -> isNeList#(ok(X)) -> isNeList#(X) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(isPal(V)) -> isNePal#(V) -> isNePal#(ok(X)) -> isNePal#(X) active#(isNePal(__(I,__(P,I)))) -> isPal#(P) -> isPal#(ok(X)) -> isPal#(X) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) -> isQid#(ok(X)) -> isQid#(X) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) -> and#(mark(X1),X2) -> and#(X1,X2) active#(isNePal(V)) -> isQid#(V) -> isQid#(ok(X)) -> isQid#(X) active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) -> and#(mark(X1),X2) -> and#(X1,X2) active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) -> and#(mark(X1),X2) -> and#(X1,X2) active#(isNeList(__(V1,V2))) -> isList#(V2) -> isList#(ok(X)) -> isList#(X) active#(isNeList(__(V1,V2))) -> isList#(V1) -> isList#(ok(X)) -> isList#(X) active#(isNeList(__(V1,V2))) -> isNeList#(V2) -> isNeList#(ok(X)) -> isNeList#(X) active#(isNeList(__(V1,V2))) -> isNeList#(V1) -> isNeList#(ok(X)) -> isNeList#(X) active#(isNeList(V)) -> isQid#(V) -> isQid#(ok(X)) -> isQid#(X) active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) -> and#(ok(X1),ok(X2)) -> and#(X1,X2) active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) -> and#(mark(X1),X2) -> and#(X1,X2) active#(isList(__(V1,V2))) -> isList#(V2) -> isList#(ok(X)) -> isList#(X) active#(isList(__(V1,V2))) -> isList#(V1) -> isList#(ok(X)) -> isList#(X) active#(isList(V)) -> isNeList#(V) -> isNeList#(ok(X)) -> isNeList#(X) 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#(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#(isPal(V)) -> isNePal#(V) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(and(X1,X2)) -> active#(X1) -> active#(isNePal(V)) -> isQid#(V) active#(and(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) active#(and(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isNeList#(V1) active#(and(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isList#(V2) active#(and(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) active#(and(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isList#(V1) active#(and(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isNeList#(V2) active#(and(X1,X2)) -> active#(X1) -> active#(isNeList(V)) -> isQid#(V) active#(and(X1,X2)) -> active#(X1) -> active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) active#(and(X1,X2)) -> active#(X1) -> active#(isList(__(V1,V2))) -> isList#(V1) active#(and(X1,X2)) -> active#(X1) -> active#(isList(__(V1,V2))) -> isList#(V2) active#(and(X1,X2)) -> active#(X1) -> active#(isList(V)) -> isNeList#(V) 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#(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#(isPal(V)) -> isNePal#(V) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(__(X1,X2)) -> active#(X2) -> active#(isNePal(V)) -> isQid#(V) active#(__(X1,X2)) -> active#(X2) -> active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) active#(__(X1,X2)) -> active#(X2) -> active#(isNeList(__(V1,V2))) -> isNeList#(V1) active#(__(X1,X2)) -> active#(X2) -> active#(isNeList(__(V1,V2))) -> isList#(V2) active#(__(X1,X2)) -> active#(X2) -> active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) active#(__(X1,X2)) -> active#(X2) -> active#(isNeList(__(V1,V2))) -> isList#(V1) active#(__(X1,X2)) -> active#(X2) -> active#(isNeList(__(V1,V2))) -> isNeList#(V2) active#(__(X1,X2)) -> active#(X2) -> active#(isNeList(V)) -> isQid#(V) active#(__(X1,X2)) -> active#(X2) -> active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) active#(__(X1,X2)) -> active#(X2) -> active#(isList(__(V1,V2))) -> isList#(V1) active#(__(X1,X2)) -> active#(X2) -> active#(isList(__(V1,V2))) -> isList#(V2) active#(__(X1,X2)) -> active#(X2) -> active#(isList(V)) -> isNeList#(V) 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#(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#(isPal(V)) -> isNePal#(V) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPal(P)) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(__(X1,X2)) -> active#(X1) -> active#(isNePal(V)) -> isQid#(V) active#(__(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> and#(isNeList(V1),isList(V2)) active#(__(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isNeList#(V1) active#(__(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isList#(V2) active#(__(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> and#(isList(V1),isNeList(V2)) active#(__(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isList#(V1) active#(__(X1,X2)) -> active#(X1) -> active#(isNeList(__(V1,V2))) -> isNeList#(V2) active#(__(X1,X2)) -> active#(X1) -> active#(isNeList(V)) -> isQid#(V) active#(__(X1,X2)) -> active#(X1) -> active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) active#(__(X1,X2)) -> active#(X1) -> active#(isList(__(V1,V2))) -> isList#(V1) active#(__(X1,X2)) -> active#(X1) -> active#(isList(__(V1,V2))) -> isList#(V2) active#(__(X1,X2)) -> active#(X1) -> active#(isList(V)) -> isNeList#(V) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(X1,X2)) -> active#(X1) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) SCC Processor: #sccs: 10 #rules: 24 #arcs: 326/2916 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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) active#(and(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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) = 1, [proper](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = x0 + 1, [isNePal](x0) = x0 + 1, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x0 + x1 + 1, [tt] = 1, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(__(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2) active#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) 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 + 2 >= X = mark(X) active(isList(V)) = V >= V = mark(isNeList(V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V + 1 >= V = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= I + P + 2 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V + 1 >= V + 1 = mark(isNePal(V)) active(isPal(nil())) = 2 >= 1 = mark(tt()) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 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) __(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)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(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()) = 1 >= 1 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = 3 >= 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 3 >= 1 = ok(and(X1,X2)) isList(ok(X)) = 1 >= 1 = ok(isList(X)) isNeList(ok(X)) = 1 >= 1 = ok(isNeList(X)) isQid(ok(X)) = 1 >= 1 = ok(isQid(X)) isNePal(ok(X)) = 2 >= 1 = ok(isNePal(X)) isPal(ok(X)) = 2 >= 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) proper#(isList(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) proper#(isPal(X)) -> 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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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, [u] = 1, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0 + 1, [isNePal](x0) = x0, [isQid](x0) = x0 + 1, [isNeList](x0) = x0 + 1, [isList](x0) = x0 + 1, [and](x0, x1) = x0 + x1 + 1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: proper#(__(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(__(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(and(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(isList(X)) = X + 2 >= X + 1 = proper#(X) proper#(isNeList(X)) = X + 2 >= X + 1 = proper#(X) proper#(isQid(X)) = X + 2 >= X + 1 = proper#(X) proper#(isNePal(X)) = X + 1 >= X + 1 = proper#(X) proper#(isPal(X)) = X + 2 >= X + 1 = proper#(X) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= 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 + 1 >= 0 = mark(X) active(isList(V)) = V + 1 >= 0 = mark(isNeList(V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V + 1 >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V + 1 >= 0 = mark(isNePal(V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 2 >= 0 = mark(tt()) active(isQid(u())) = 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 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 + 1 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(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(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: proper#(isNePal(X)) -> proper#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isNePal](x0) = x0 + 1, [isQid](x0) = 0, [isNeList](x0) = 0, [isList](x0) = 0, [and](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = 0, [__](x0, x1) = 0 orientation: proper#(isNePal(X)) = X + 2 >= X + 1 = proper#(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(isList(V)) = 0 >= 0 = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 0 >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 0 >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 0 >= 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = 0 >= 0 = __(active(X1),X2) active(__(X1,X2)) = 0 >= 0 = __(X1,active(X2)) active(and(X1,X2)) = 0 >= 0 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) 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(isList(X)) = 0 >= 0 = isList(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 0 >= 0 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 0 >= 0 = ok(and(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isPal#(ok(X)) -> isPal#(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isPal#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isPal#(ok(X)) = X + 2 >= X + 1 = isPal#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) 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(isList(X)) = 1 >= 1 = isList(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed 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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isNePal#(ok(X)) = X + 2 >= X + 1 = isNePal#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) 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(isList(X)) = 1 >= 1 = isList(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isQid#(ok(X)) -> isQid#(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isQid#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isQid#(ok(X)) = X + 2 >= X + 1 = isQid#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) 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(isList(X)) = 1 >= 1 = isList(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNeList#(ok(X)) -> isNeList#(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isNeList#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isNeList#(ok(X)) = X + 2 >= X + 1 = isNeList#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) 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(isList(X)) = 1 >= 1 = isList(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isList#(ok(X)) -> isList#(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isList#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: isList#(ok(X)) = X + 2 >= X + 1 = isList#(X) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) 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(isList(X)) = 1 >= 1 = isList(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(ok(X1),ok(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [and#](x0, x1) = x1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: and#(mark(X1),X2) = X2 >= X2 = and#(X1,X2) and#(ok(X1),ok(X2)) = X2 + 1 >= X2 = and#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) 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(isList(X)) = 1 >= 1 = isList(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [and#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = 1, [proper](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0, [and](x0, x1) = x0 + x1, [tt] = 1, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: and#(mark(X1),X2) = X1 + 2 >= X1 + 1 = and#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= X + 1 = mark(X) active(__(nil(),X)) = X + 2 >= X + 1 = mark(X) active(and(tt(),X)) = X + 2 >= X + 1 = mark(X) active(isList(V)) = V + 1 >= V + 1 = mark(isNeList(V)) active(isList(nil())) = 2 >= 2 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V + 1 >= V + 1 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V + 1 >= V + 1 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 1 >= I + P + 1 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V + 1 >= V + 1 = mark(isNePal(V)) active(isPal(nil())) = 2 >= 2 = mark(tt()) active(isQid(a())) = 2 >= 2 = mark(tt()) active(isQid(e())) = 2 >= 2 = mark(tt()) active(isQid(i())) = 2 >= 2 = mark(tt()) active(isQid(o())) = 2 >= 2 = mark(tt()) active(isQid(u())) = 2 >= 2 = 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) __(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)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(isPal(X)) = X >= X = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = 2 >= 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 2 >= 1 = ok(and(X1,X2)) isList(ok(X)) = 1 >= 1 = ok(isList(X)) isNeList(ok(X)) = 1 >= 1 = ok(isNeList(X)) isQid(ok(X)) = 1 >= 1 = ok(isQid(X)) isNePal(ok(X)) = 1 >= 1 = ok(isNePal(X)) isPal(ok(X)) = 1 >= 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x0 + x1 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isNePal](x0) = 0, [isQid](x0) = 0, [isNeList](x0) = 0, [isList](x0) = 0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: __#(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 1 = __#(X1,X2) __#(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 1 = __#(X1,X2) __#(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __#(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(isList(V)) = 1 >= 1 = mark(isNeList(V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 1 >= 1 = mark(isQid(V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 1 >= 1 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 1 >= 1 = mark(isNePal(V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 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) __(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)) 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(isList(X)) = 0 >= 0 = isList(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(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) 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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0 + 1, [and](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: __#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = __#(X1,X2) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V + 1 >= 0 = mark(isNeList(V)) active(isList(nil())) = 2 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 + 1 >= 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= 0 = mark(isNePal(V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(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()) = 1 >= 1 = ok(tt()) proper(isList(X)) = X + 2 >= X + 2 = isList(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isList(ok(X)) = X + 2 >= X + 2 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(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(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) 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(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed