YES 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Proof: DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(__(X,nil())) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> isNeList#(V) active#(isList(V)) -> mark#(isNeList(V)) active#(isList(nil())) -> mark#(tt()) active#(isList(__(V1,V2))) -> isList#(V2) active#(isList(__(V1,V2))) -> isList#(V1) active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) active#(isNeList(V)) -> isQid#(V) active#(isNeList(V)) -> mark#(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))) -> mark#(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#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) active#(isNePal(V)) -> isQid#(V) active#(isNePal(V)) -> mark#(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#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) active#(isPal(V)) -> isNePal#(V) 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()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isList(X)) -> active#(isList(X)) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(isQid(X)) -> active#(isQid(X)) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(isPal(X)) -> active#(isPal(X)) mark#(a()) -> active#(a()) mark#(e()) -> active#(e()) mark#(i()) -> active#(i()) mark#(o()) -> active#(o()) mark#(u()) -> active#(u()) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isList#(mark(X)) -> isList#(X) isList#(active(X)) -> isList#(X) isNeList#(mark(X)) -> isNeList#(X) isNeList#(active(X)) -> isNeList#(X) isQid#(mark(X)) -> isQid#(X) isQid#(active(X)) -> isQid#(X) isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) isPal#(mark(X)) -> isPal#(X) isPal#(active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(__(X,nil())) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(and(tt(),X)) -> mark#(X) active#(isList(V)) -> isNeList#(V) active#(isList(V)) -> mark#(isNeList(V)) active#(isList(nil())) -> mark#(tt()) active#(isList(__(V1,V2))) -> isList#(V2) active#(isList(__(V1,V2))) -> isList#(V1) active#(isList(__(V1,V2))) -> and#(isList(V1),isList(V2)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) active#(isNeList(V)) -> isQid#(V) active#(isNeList(V)) -> mark#(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))) -> mark#(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#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) active#(isNePal(V)) -> isQid#(V) active#(isNePal(V)) -> mark#(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#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) active#(isPal(V)) -> isNePal#(V) 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()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isList(X)) -> active#(isList(X)) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(isQid(X)) -> active#(isQid(X)) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(isPal(X)) -> active#(isPal(X)) mark#(a()) -> active#(a()) mark#(e()) -> active#(e()) mark#(i()) -> active#(i()) mark#(o()) -> active#(o()) mark#(u()) -> active#(u()) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isList#(mark(X)) -> isList#(X) isList#(active(X)) -> isList#(X) isNeList#(mark(X)) -> isNeList#(X) isNeList#(active(X)) -> isNeList#(X) isQid#(mark(X)) -> isQid#(X) isQid#(active(X)) -> isQid#(X) isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) isPal#(mark(X)) -> isPal#(X) isPal#(active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) graph: ... SCC Processor: #sccs: 8 #rules: 54 #arcs: 1044/5476 DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(isList(V)) -> mark#(isNeList(V)) mark#(isList(X)) -> active#(isList(X)) active#(isList(nil())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(isQid(X)) -> active#(isQid(X)) active#(isNeList(V)) -> mark#(isQid(V)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(isPal(X)) -> active#(isPal(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(a()) -> active#(a()) active#(isNePal(V)) -> mark#(isQid(V)) mark#(e()) -> active#(e()) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(i()) -> active#(i()) active#(isPal(V)) -> mark#(isNePal(V)) mark#(o()) -> active#(o()) 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()) 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) EDG Processor: DPs: mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(isList(V)) -> mark#(isNeList(V)) mark#(isList(X)) -> active#(isList(X)) active#(isList(nil())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(isQid(X)) -> active#(isQid(X)) active#(isNeList(V)) -> mark#(isQid(V)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(isPal(X)) -> active#(isPal(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(a()) -> active#(a()) active#(isNePal(V)) -> mark#(isQid(V)) mark#(e()) -> active#(e()) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(i()) -> active#(i()) active#(isPal(V)) -> mark#(isNePal(V)) mark#(o()) -> active#(o()) 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()) 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) graph: mark#(isPal(X)) -> active#(isPal(X)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isPal(X)) -> active#(isPal(X)) -> active#(__(X,nil())) -> mark#(X) mark#(isPal(X)) -> active#(isPal(X)) -> active#(__(nil(),X)) -> mark#(X) mark#(isPal(X)) -> active#(isPal(X)) -> active#(and(tt(),X)) -> mark#(X) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isList(V)) -> mark#(isNeList(V)) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isList(nil())) -> mark#(tt()) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isNeList(V)) -> mark#(isQid(V)) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isNePal(V)) -> mark#(isQid(V)) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isPal(V)) -> mark#(isNePal(V)) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isPal(nil())) -> mark#(tt()) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isQid(a())) -> mark#(tt()) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isQid(e())) -> mark#(tt()) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isQid(i())) -> mark#(tt()) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isQid(o())) -> mark#(tt()) mark#(isPal(X)) -> active#(isPal(X)) -> active#(isQid(u())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(__(X,nil())) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(__(nil(),X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(and(tt(),X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isList(V)) -> mark#(isNeList(V)) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isList(nil())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isNeList(V)) -> mark#(isQid(V)) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isNePal(V)) -> mark#(isQid(V)) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isPal(V)) -> mark#(isNePal(V)) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isPal(nil())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isQid(a())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isQid(e())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isQid(i())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isQid(o())) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(X)) -> active#(isQid(u())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isQid(X)) -> active#(isQid(X)) -> active#(__(X,nil())) -> mark#(X) mark#(isQid(X)) -> active#(isQid(X)) -> active#(__(nil(),X)) -> mark#(X) mark#(isQid(X)) -> active#(isQid(X)) -> active#(and(tt(),X)) -> mark#(X) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isList(V)) -> mark#(isNeList(V)) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isList(nil())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isNeList(V)) -> mark#(isQid(V)) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isNePal(V)) -> mark#(isQid(V)) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isPal(V)) -> mark#(isNePal(V)) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isPal(nil())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isQid(a())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isQid(e())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isQid(i())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isQid(o())) -> mark#(tt()) mark#(isQid(X)) -> active#(isQid(X)) -> active#(isQid(u())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(__(X,nil())) -> mark#(X) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(__(nil(),X)) -> mark#(X) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(and(tt(),X)) -> mark#(X) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isList(V)) -> mark#(isNeList(V)) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isList(nil())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isNeList(V)) -> mark#(isQid(V)) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isNePal(V)) -> mark#(isQid(V)) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isPal(V)) -> mark#(isNePal(V)) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isPal(nil())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isQid(a())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isQid(e())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isQid(i())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isQid(o())) -> mark#(tt()) mark#(isNeList(X)) -> active#(isNeList(X)) -> active#(isQid(u())) -> mark#(tt()) mark#(isList(X)) -> active#(isList(X)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isList(X)) -> active#(isList(X)) -> active#(__(X,nil())) -> mark#(X) mark#(isList(X)) -> active#(isList(X)) -> active#(__(nil(),X)) -> mark#(X) mark#(isList(X)) -> active#(isList(X)) -> active#(and(tt(),X)) -> mark#(X) mark#(isList(X)) -> active#(isList(X)) -> active#(isList(V)) -> mark#(isNeList(V)) mark#(isList(X)) -> active#(isList(X)) -> active#(isList(nil())) -> mark#(tt()) mark#(isList(X)) -> active#(isList(X)) -> active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(isList(X)) -> active#(isList(X)) -> active#(isNeList(V)) -> mark#(isQid(V)) mark#(isList(X)) -> active#(isList(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(isList(X)) -> active#(isList(X)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(isList(X)) -> active#(isList(X)) -> active#(isNePal(V)) -> mark#(isQid(V)) mark#(isList(X)) -> active#(isList(X)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(isList(X)) -> active#(isList(X)) -> active#(isPal(V)) -> mark#(isNePal(V)) mark#(isList(X)) -> active#(isList(X)) -> active#(isPal(nil())) -> mark#(tt()) mark#(isList(X)) -> active#(isList(X)) -> active#(isQid(a())) -> mark#(tt()) mark#(isList(X)) -> active#(isList(X)) -> active#(isQid(e())) -> mark#(tt()) mark#(isList(X)) -> active#(isList(X)) -> active#(isQid(i())) -> mark#(tt()) mark#(isList(X)) -> active#(isList(X)) -> active#(isQid(o())) -> mark#(tt()) mark#(isList(X)) -> active#(isList(X)) -> active#(isQid(u())) -> mark#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isList(X)) -> active#(isList(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNeList(X)) -> active#(isNeList(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isQid(X)) -> active#(isQid(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isPal(X)) -> active#(isPal(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(a()) -> active#(a()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(e()) -> active#(e()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(i()) -> active#(i()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(o()) -> active#(o()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(u()) -> active#(u()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(X,nil())) -> mark#(X) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(nil(),X)) -> mark#(X) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(and(tt(),X)) -> mark#(X) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isList(V)) -> mark#(isNeList(V)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isList(nil())) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNeList(V)) -> mark#(isQid(V)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNePal(V)) -> mark#(isQid(V)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isPal(V)) -> mark#(isNePal(V)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isPal(nil())) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isQid(a())) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isQid(e())) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isQid(i())) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isQid(o())) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isQid(u())) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isList(X)) -> active#(isList(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNeList(X)) -> active#(isNeList(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isQid(X)) -> active#(isQid(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> active#(isNePal(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isPal(X)) -> active#(isPal(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(a()) -> active#(a()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(e()) -> active#(e()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(i()) -> active#(i()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(o()) -> active#(o()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(u()) -> active#(u()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isList(X)) -> active#(isList(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNeList(X)) -> active#(isNeList(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isQid(X)) -> active#(isQid(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isPal(X)) -> active#(isPal(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(a()) -> active#(a()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(e()) -> active#(e()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(i()) -> active#(i()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(o()) -> active#(o()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(u()) -> active#(u()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(X,nil())) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(nil(),X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(and(tt(),X)) -> mark#(X) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isList(V)) -> mark#(isNeList(V)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isList(nil())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNeList(V)) -> mark#(isQid(V)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNePal(V)) -> mark#(isQid(V)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isPal(V)) -> mark#(isNePal(V)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isPal(nil())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isQid(a())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isQid(e())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isQid(i())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isQid(o())) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isQid(u())) -> mark#(tt()) active#(isPal(nil())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(__(X1,X2)) -> mark#(X2) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(__(X1,X2)) -> mark#(X1) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(and(X1,X2)) -> mark#(X1) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(isList(X)) -> active#(isList(X)) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isPal(V)) -> mark#(isNePal(V)) -> mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(__(X1,X2)) -> mark#(X2) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(isList(X)) -> active#(isList(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) -> mark#(isPal(X)) -> active#(isPal(X)) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(__(X1,X2)) -> mark#(X2) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(isList(X)) -> active#(isList(X)) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNePal(V)) -> mark#(isQid(V)) -> mark#(isPal(X)) -> active#(isPal(X)) active#(isQid(u())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isQid(o())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isQid(i())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isQid(e())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isQid(a())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(__(X1,X2)) -> mark#(X2) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(isList(X)) -> active#(isList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) -> mark#(isPal(X)) -> active#(isPal(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(__(X1,X2)) -> mark#(X2) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(isList(X)) -> active#(isList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) -> mark#(isPal(X)) -> active#(isPal(X)) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(__(X1,X2)) -> mark#(X2) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(isList(X)) -> active#(isList(X)) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNeList(V)) -> mark#(isQid(V)) -> mark#(isPal(X)) -> active#(isPal(X)) active#(isList(nil())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(__(X1,X2)) -> mark#(X2) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(__(X1,X2)) -> mark#(X1) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(and(X1,X2)) -> mark#(X1) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(isList(X)) -> active#(isList(X)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) -> mark#(isPal(X)) -> active#(isPal(X)) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(__(X1,X2)) -> mark#(X2) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(__(X1,X2)) -> mark#(X1) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(and(X1,X2)) -> mark#(X1) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(isList(X)) -> active#(isList(X)) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(isQid(X)) -> active#(isQid(X)) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(isList(V)) -> mark#(isNeList(V)) -> mark#(isPal(X)) -> active#(isPal(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) -> mark#(isList(X)) -> active#(isList(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(isQid(X)) -> active#(isQid(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(isPal(X)) -> active#(isPal(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(a()) -> active#(a()) active#(and(tt(),X)) -> mark#(X) -> mark#(e()) -> active#(e()) active#(and(tt(),X)) -> mark#(X) -> mark#(i()) -> active#(i()) active#(and(tt(),X)) -> mark#(X) -> mark#(o()) -> active#(o()) active#(and(tt(),X)) -> mark#(X) -> mark#(u()) -> active#(u()) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(nil(),X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(nil(),X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(__(nil(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) active#(__(nil(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(nil(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(__(nil(),X)) -> mark#(X) -> mark#(isList(X)) -> active#(isList(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(isQid(X)) -> active#(isQid(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(isPal(X)) -> active#(isPal(X)) active#(__(nil(),X)) -> mark#(X) -> mark#(a()) -> active#(a()) active#(__(nil(),X)) -> mark#(X) -> mark#(e()) -> active#(e()) active#(__(nil(),X)) -> mark#(X) -> mark#(i()) -> active#(i()) active#(__(nil(),X)) -> mark#(X) -> mark#(o()) -> active#(o()) active#(__(nil(),X)) -> mark#(X) -> mark#(u()) -> active#(u()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isList(X)) -> active#(isList(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isQid(X)) -> active#(isQid(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isPal(X)) -> active#(isPal(X)) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(X,nil())) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(X,nil())) -> mark#(X) -> mark#(nil()) -> active#(nil()) active#(__(X,nil())) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) active#(__(X,nil())) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(X,nil())) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(__(X,nil())) -> mark#(X) -> mark#(isList(X)) -> active#(isList(X)) active#(__(X,nil())) -> mark#(X) -> mark#(isNeList(X)) -> active#(isNeList(X)) active#(__(X,nil())) -> mark#(X) -> mark#(isQid(X)) -> active#(isQid(X)) active#(__(X,nil())) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(X)) active#(__(X,nil())) -> mark#(X) -> mark#(isPal(X)) -> active#(isPal(X)) active#(__(X,nil())) -> mark#(X) -> mark#(a()) -> active#(a()) active#(__(X,nil())) -> mark#(X) -> mark#(e()) -> active#(e()) active#(__(X,nil())) -> mark#(X) -> mark#(i()) -> active#(i()) active#(__(X,nil())) -> mark#(X) -> mark#(o()) -> active#(o()) active#(__(X,nil())) -> mark#(X) -> mark#(u()) -> active#(u()) SCC Processor: #sccs: 1 #rules: 22 #arcs: 332/1296 DPs: mark#(isPal(X)) -> active#(isPal(X)) active#(isPal(V)) -> mark#(isNePal(V)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(isQid(X)) -> active#(isQid(X)) active#(isNePal(V)) -> mark#(isQid(V)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(isList(X)) -> active#(isList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNeList(V)) -> mark#(isQid(V)) mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) active#(isList(V)) -> mark#(isNeList(V)) active#(and(tt(),X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 6x0, [active#](x0) = 6x0, [u] = 6, [o] = 2, [i] = 7, [e] = 5, [a] = 0, [isPal](x0) = x0 + 0, [isNePal](x0) = x0 + 0, [isQid](x0) = x0, [isNeList](x0) = 1x0, [isList](x0) = 1x0, [and](x0, x1) = x0 + x1 + 0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 0, [active](x0) = x0 + 0, [__](x0, x1) = x0 + x1 + 0 orientation: mark#(isPal(X)) = 6X + 6 >= 6X + 6 = active#(isPal(X)) active#(isPal(V)) = 6V + 6 >= 6V + 6 = mark#(isNePal(V)) mark#(isNePal(X)) = 6X + 6 >= 6X + 6 = active#(isNePal(X)) active#(isNePal(__(I,__(P,I)))) = 6I + 6P + 6 >= 6I + 6P + 6 = mark#(and(isQid(I),isPal(P))) mark#(isQid(X)) = 6X >= 6X = active#(isQid(X)) active#(isNePal(V)) = 6V + 6 >= 6V = mark#(isQid(V)) mark#(isNeList(X)) = 7X >= 7X = active#(isNeList(X)) active#(isNeList(__(V1,V2))) = 7V1 + 7V2 + 7 >= 7V1 + 7V2 + 6 = mark#(and(isNeList(V1),isList(V2))) mark#(isList(X)) = 7X >= 7X = active#(isList(X)) active#(isNeList(__(V1,V2))) = 7V1 + 7V2 + 7 >= 7V1 + 7V2 + 6 = mark#(and(isList(V1),isNeList(V2))) mark#(and(X1,X2)) = 6X1 + 6X2 + 6 >= 6X1 + 6X2 + 6 = active#(and(mark(X1),X2)) active#(isNeList(V)) = 7V >= 6V = mark#(isQid(V)) mark#(and(X1,X2)) = 6X1 + 6X2 + 6 >= 6X1 = mark#(X1) mark#(__(X1,X2)) = 6X1 + 6X2 + 6 >= 6X1 + 6X2 + 6 = active#(__(mark(X1),mark(X2))) active#(isList(__(V1,V2))) = 7V1 + 7V2 + 7 >= 7V1 + 7V2 + 6 = mark#(and(isList(V1),isList(V2))) mark#(__(X1,X2)) = 6X1 + 6X2 + 6 >= 6X1 = mark#(X1) mark#(__(X1,X2)) = 6X1 + 6X2 + 6 >= 6X2 = mark#(X2) active#(isList(V)) = 7V >= 7V = mark#(isNeList(V)) active#(and(tt(),X)) = 6X + 6 >= 6X = mark#(X) active#(__(nil(),X)) = 6X + 6 >= 6X = mark#(X) active#(__(X,nil())) = 6X + 6 >= 6X = mark#(X) active#(__(__(X,Y),Z)) = 6X + 6Y + 6Z + 6 >= 6X + 6Y + 6Z + 6 = mark#(__(X,__(Y,Z))) active(__(__(X,Y),Z)) = X + Y + Z + 0 >= X + Y + Z + 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 0 >= X + 0 = mark(X) active(__(nil(),X)) = X + 0 >= X + 0 = mark(X) active(and(tt(),X)) = X + 0 >= X + 0 = mark(X) active(isList(V)) = 1V + 0 >= 1V + 0 = mark(isNeList(V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 1V1 + 1V2 + 1 >= 1V1 + 1V2 + 0 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 1V + 0 >= V + 0 = mark(isQid(V)) active(isNeList(__(V1,V2))) = 1V1 + 1V2 + 1 >= 1V1 + 1V2 + 0 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 1V1 + 1V2 + 1 >= 1V1 + 1V2 + 0 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V + 0 >= V + 0 = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = I + P + 0 >= I + P + 0 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V + 0 >= V + 0 = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 5 >= 0 = mark(tt()) active(isQid(i())) = 7 >= 0 = mark(tt()) active(isQid(o())) = 2 >= 0 = mark(tt()) active(isQid(u())) = 6 >= 0 = mark(tt()) mark(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(and(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(isList(X)) = 1X + 0 >= 1X + 0 = active(isList(X)) mark(isNeList(X)) = 1X + 0 >= 1X + 0 = active(isNeList(X)) mark(isQid(X)) = X + 0 >= X + 0 = active(isQid(X)) mark(isNePal(X)) = X + 0 >= X + 0 = active(isNePal(X)) mark(isPal(X)) = X + 0 >= X + 0 = active(isPal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 5 >= 5 = active(e()) mark(i()) = 7 >= 7 = active(i()) mark(o()) = 2 >= 2 = active(o()) mark(u()) = 6 >= 6 = active(u()) __(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2) and(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) isList(mark(X)) = 1X + 1 >= 1X = isList(X) isList(active(X)) = 1X + 1 >= 1X = isList(X) isNeList(mark(X)) = 1X + 1 >= 1X = isNeList(X) isNeList(active(X)) = 1X + 1 >= 1X = isNeList(X) isQid(mark(X)) = X + 0 >= X = isQid(X) isQid(active(X)) = X + 0 >= X = isQid(X) isNePal(mark(X)) = X + 0 >= X + 0 = isNePal(X) isNePal(active(X)) = X + 0 >= X + 0 = isNePal(X) isPal(mark(X)) = X + 0 >= X + 0 = isPal(X) isPal(active(X)) = X + 0 >= X + 0 = isPal(X) problem: DPs: mark#(isPal(X)) -> active#(isPal(X)) active#(isPal(V)) -> mark#(isNePal(V)) mark#(isNePal(X)) -> active#(isNePal(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(and(isQid(I),isPal(P))) mark#(isQid(X)) -> active#(isQid(X)) active#(isNePal(V)) -> mark#(isQid(V)) mark#(isNeList(X)) -> active#(isNeList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isNeList(V1),isList(V2))) mark#(isList(X)) -> active#(isList(X)) active#(isNeList(__(V1,V2))) -> mark#(and(isList(V1),isNeList(V2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isList(__(V1,V2))) -> mark#(and(isList(V1),isList(V2))) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) active#(isList(V)) -> mark#(isNeList(V)) active#(and(tt(),X)) -> mark#(X) active#(__(nil(),X)) -> mark#(X) active#(__(X,nil())) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) KBO Processor: argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = 0 pi(nil) = [] pi(tt) = [] pi(and) = [0,1] pi(isList) = 0 pi(isNeList) = 0 pi(isQid) = 0 pi(isNePal) = 0 pi(isPal) = 0 pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(active#) = 0 pi(mark#) = 0 weight function: w0 = 1 w(mark#) = w(u) = w(o) = w(i) = w(e) = w(a) = w(and) = w(tt) = w( nil) = w(active) = w(__) = 1 w(active#) = w(isPal) = w(isNePal) = w(isQid) = w(isNeList) = w( isList) = w(mark) = 0 precedence: i > o ~ e ~ a > u ~ nil > __ > mark# ~ active# ~ isPal ~ isNePal ~ isQid ~ isNeList ~ isList ~ and ~ tt ~ mark ~ active problem: DPs: mark#(isPal(X)) -> active#(isPal(X)) active#(isPal(V)) -> mark#(isNePal(V)) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(isQid(X)) -> active#(isQid(X)) active#(isNePal(V)) -> mark#(isQid(V)) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(isList(X)) -> active#(isList(X)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isList(V)) -> mark#(isNeList(V)) 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) KBO Processor: argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = 0 pi(nil) = [] pi(tt) = [] pi(and) = [1] pi(isList) = 0 pi(isNeList) = 0 pi(isQid) = 0 pi(isNePal) = 0 pi(isPal) = [0] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(active#) = 0 pi(mark#) = 0 weight function: w0 = 1 w(active#) = w(u) = w(o) = w(i) = w(e) = w(a) = w(isPal) = w( isQid) = w(and) = w(tt) = w(nil) = w(active) = 1 w(mark#) = w(isNePal) = w(isNeList) = w(isList) = w(mark) = w( __) = 0 precedence: u > e ~ __ > o ~ i ~ a ~ nil > mark# ~ active# ~ isPal ~ isNePal ~ isQid ~ isNeList ~ isList ~ and ~ tt ~ mark ~ active problem: DPs: mark#(isPal(X)) -> active#(isPal(X)) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(isQid(X)) -> active#(isQid(X)) active#(isNePal(V)) -> mark#(isQid(V)) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(isList(X)) -> active#(isList(X)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isList(V)) -> mark#(isNeList(V)) 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) KBO Processor: argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = 0 pi(nil) = [] pi(tt) = [] pi(and) = 1 pi(isList) = [0] pi(isNeList) = 0 pi(isQid) = 0 pi(isNePal) = 0 pi(isPal) = 0 pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(active#) = 0 pi(mark#) = 0 weight function: w0 = 1 w(u) = w(o) = w(i) = w(e) = w(a) = w(tt) = w(nil) = w(active) = 1 w(mark#) = w(active#) = w(isPal) = w(isNePal) = w(isQid) = w( isNeList) = w(isList) = w(and) = w(mark) = w(__) = 0 precedence: mark > u ~ o ~ i ~ e ~ a ~ isList ~ nil ~ __ > mark# ~ active# ~ isPal ~ isNePal ~ isQid ~ isNeList ~ and ~ tt ~ active problem: DPs: mark#(isPal(X)) -> active#(isPal(X)) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(isQid(X)) -> active#(isQid(X)) active#(isNePal(V)) -> mark#(isQid(V)) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(isList(X)) -> active#(isList(X)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) KBO Processor: argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = 0 pi(nil) = [] pi(tt) = [] pi(and) = [1] pi(isList) = 0 pi(isNeList) = 0 pi(isQid) = 0 pi(isNePal) = [0] pi(isPal) = [0] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(active#) = 0 pi(mark#) = 0 weight function: w0 = 1 w(mark#) = w(u) = w(o) = w(i) = w(e) = w(a) = w(isPal) = w( isNePal) = w(and) = w(tt) = w(nil) = w(active) = 1 w(active#) = w(isQid) = w(isNeList) = w(isList) = w(mark) = w( __) = 0 precedence: u > isPal ~ __ > o ~ i ~ e ~ a ~ nil > mark# ~ active# ~ isNePal ~ isQid ~ isNeList ~ isList ~ and ~ tt ~ mark ~ active problem: DPs: mark#(isPal(X)) -> active#(isPal(X)) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(isQid(X)) -> active#(isQid(X)) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(isList(X)) -> active#(isList(X)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) SCC Processor: #sccs: 0 #rules: 0 #arcs: 234/49 DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(__#) = 1 problem: DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(__#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Qed DPs: isNeList#(mark(X)) -> isNeList#(X) isNeList#(active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(isNeList#) = 0 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Qed DPs: isList#(mark(X)) -> isList#(X) isList#(active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(isList#) = 0 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Qed DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(and#) = 1 problem: DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(and#) = 0 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Qed DPs: isQid#(mark(X)) -> isQid#(X) isQid#(active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(isQid#) = 0 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Qed DPs: isPal#(mark(X)) -> isPal#(X) isPal#(active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(isPal#) = 0 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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Qed DPs: isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Subterm Criterion Processor: simple projection: pi(isNePal#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(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()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Qed