YES Problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) -> a__isQid(V) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isPal(nil()) -> tt() a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Proof: DP Processor: DPs: a____#(__(X,Y),Z) -> mark#(Z) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) a__and#(tt(),X) -> mark#(X) a__isList#(V) -> a__isNeList#(V) a__isList#(__(V1,V2)) -> a__isList#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2)) a__isNeList#(V) -> a__isQid#(V) a__isNeList#(__(V1,V2)) -> a__isList#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2)) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2)) a__isNePal#(V) -> a__isQid#(V) a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPal(P)) a__isPal#(V) -> a__isNePal#(V) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(isNeList(X)) -> a__isNeList#(X) mark#(isQid(X)) -> a__isQid#(X) mark#(isNePal(X)) -> a__isNePal#(X) mark#(isPal(X)) -> a__isPal#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) -> a__isQid(V) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isPal(nil()) -> tt() a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) TDG Processor: DPs: a____#(__(X,Y),Z) -> mark#(Z) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) a__and#(tt(),X) -> mark#(X) a__isList#(V) -> a__isNeList#(V) a__isList#(__(V1,V2)) -> a__isList#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2)) a__isNeList#(V) -> a__isQid#(V) a__isNeList#(__(V1,V2)) -> a__isList#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2)) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2)) a__isNePal#(V) -> a__isQid#(V) a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPal(P)) a__isPal#(V) -> a__isNePal#(V) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) mark#(isNeList(X)) -> a__isNeList#(X) mark#(isQid(X)) -> a__isQid#(X) mark#(isNePal(X)) -> a__isNePal#(X) mark#(isPal(X)) -> a__isPal#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) -> a__isQid(V) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isPal(nil()) -> tt() a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) graph: a__isPal#(V) -> a__isNePal#(V) -> a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPal(P)) a__isPal#(V) -> a__isNePal#(V) -> a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) a__isPal#(V) -> a__isNePal#(V) -> a__isNePal#(V) -> a__isQid#(V) a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPal(P)) -> a__and#(tt(),X) -> mark#(X) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) -> a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2)) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) -> a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) -> a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2)) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) -> a__isNeList#(__(V1,V2)) -> a__isList#(V1) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) -> a__isNeList#(V) -> a__isQid#(V) a__isNeList#(__(V1,V2)) -> a__isList#(V1) -> a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2)) a__isNeList#(__(V1,V2)) -> a__isList#(V1) -> a__isList#(__(V1,V2)) -> a__isList#(V1) a__isNeList#(__(V1,V2)) -> a__isList#(V1) -> a__isList#(V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2)) -> a__and#(tt(),X) -> mark#(X) a__isList#(__(V1,V2)) -> a__isList#(V1) -> a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2)) a__isList#(__(V1,V2)) -> a__isList#(V1) -> a__isList#(__(V1,V2)) -> a__isList#(V1) a__isList#(__(V1,V2)) -> a__isList#(V1) -> a__isList#(V) -> a__isNeList#(V) a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2)) -> a__and#(tt(),X) -> mark#(X) a__isList#(V) -> a__isNeList#(V) -> a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2)) a__isList#(V) -> a__isNeList#(V) -> a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) a__isList#(V) -> a__isNeList#(V) -> a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2)) a__isList#(V) -> a__isNeList#(V) -> a__isNeList#(__(V1,V2)) -> a__isList#(V1) a__isList#(V) -> a__isNeList#(V) -> a__isNeList#(V) -> a__isQid#(V) a__and#(tt(),X) -> mark#(X) -> mark#(isPal(X)) -> a__isPal#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isNePal(X)) -> a__isNePal#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isQid(X)) -> a__isQid#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isNeList(X)) -> a__isNeList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isList(X)) -> a__isList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a__and#(tt(),X) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(isNePal(X)) -> a__isNePal#(X) -> a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPal(P)) mark#(isNePal(X)) -> a__isNePal#(X) -> a__isNePal#(__(I,__(P,I))) -> a__isQid#(I) mark#(isNePal(X)) -> a__isNePal#(X) -> a__isNePal#(V) -> a__isQid#(V) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) -> a__and#(tt(),X) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isPal(X)) -> a__isPal#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> a__isNePal#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isQid(X)) -> a__isQid#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNeList(X)) -> a__isNeList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isList(X)) -> a__isList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(isPal(X)) -> a__isPal#(X) -> a__isPal#(V) -> a__isNePal#(V) mark#(isNeList(X)) -> a__isNeList#(X) -> a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2)) mark#(isNeList(X)) -> a__isNeList#(X) -> a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) mark#(isNeList(X)) -> a__isNeList#(X) -> a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2)) mark#(isNeList(X)) -> a__isNeList#(X) -> a__isNeList#(__(V1,V2)) -> a__isList#(V1) mark#(isNeList(X)) -> a__isNeList#(X) -> a__isNeList#(V) -> a__isQid#(V) mark#(isList(X)) -> a__isList#(X) -> a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2)) mark#(isList(X)) -> a__isList#(X) -> a__isList#(__(V1,V2)) -> a__isList#(V1) mark#(isList(X)) -> a__isList#(X) -> a__isList#(V) -> a__isNeList#(V) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isPal(X)) -> a__isPal#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> a__isNePal#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isQid(X)) -> a__isQid#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNeList(X)) -> a__isNeList#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isList(X)) -> a__isList#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isPal(X)) -> a__isPal#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> a__isNePal#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isQid(X)) -> a__isQid#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNeList(X)) -> a__isNeList#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isList(X)) -> a__isList#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) -> a____#(nil(),X) -> mark#(X) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) -> a____#(X,nil()) -> mark#(X) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) -> a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) -> a____#(__(X,Y),Z) -> mark#(X) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) -> a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) -> a____#(__(X,Y),Z) -> mark#(Y) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) -> a____#(__(X,Y),Z) -> mark#(Z) a____#(nil(),X) -> mark#(X) -> mark#(isPal(X)) -> a__isPal#(X) a____#(nil(),X) -> mark#(X) -> mark#(isNePal(X)) -> a__isNePal#(X) a____#(nil(),X) -> mark#(X) -> mark#(isQid(X)) -> a__isQid#(X) a____#(nil(),X) -> mark#(X) -> mark#(isNeList(X)) -> a__isNeList#(X) a____#(nil(),X) -> mark#(X) -> mark#(isList(X)) -> a__isList#(X) a____#(nil(),X) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a____#(nil(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) a____#(nil(),X) -> mark#(X) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(nil(),X) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) a____#(nil(),X) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(isPal(X)) -> a__isPal#(X) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(isNePal(X)) -> a__isNePal#(X) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(isQid(X)) -> a__isQid#(X) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(isNeList(X)) -> a__isNeList#(X) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(isList(X)) -> a__isList#(X) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(and(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(__(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(Z) -> mark#(__(X1,X2)) -> mark#(X2) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(isPal(X)) -> a__isPal#(X) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(isNePal(X)) -> a__isNePal#(X) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(isQid(X)) -> a__isQid#(X) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(isNeList(X)) -> a__isNeList#(X) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(isList(X)) -> a__isList#(X) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(and(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(__(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(Y) -> mark#(__(X1,X2)) -> mark#(X2) a____#(__(X,Y),Z) -> mark#(X) -> mark#(isPal(X)) -> a__isPal#(X) a____#(__(X,Y),Z) -> mark#(X) -> mark#(isNePal(X)) -> a__isNePal#(X) a____#(__(X,Y),Z) -> mark#(X) -> mark#(isQid(X)) -> a__isQid#(X) a____#(__(X,Y),Z) -> mark#(X) -> mark#(isNeList(X)) -> a__isNeList#(X) a____#(__(X,Y),Z) -> mark#(X) -> mark#(isList(X)) -> a__isList#(X) a____#(__(X,Y),Z) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a____#(__(X,Y),Z) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(X) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) a____#(__(X,Y),Z) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) -> a____#(nil(),X) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) -> a____#(X,nil()) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) -> a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) -> a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) -> a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) -> a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) -> a____#(__(X,Y),Z) -> mark#(Z) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) -> a____#(nil(),X) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) -> a____#(X,nil()) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) -> a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) -> a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) -> a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) -> a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) -> a____#(__(X,Y),Z) -> mark#(Z) a____#(X,nil()) -> mark#(X) -> mark#(isPal(X)) -> a__isPal#(X) a____#(X,nil()) -> mark#(X) -> mark#(isNePal(X)) -> a__isNePal#(X) a____#(X,nil()) -> mark#(X) -> mark#(isQid(X)) -> a__isQid#(X) a____#(X,nil()) -> mark#(X) -> mark#(isNeList(X)) -> a__isNeList#(X) a____#(X,nil()) -> mark#(X) -> mark#(isList(X)) -> a__isList#(X) a____#(X,nil()) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a____#(X,nil()) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) a____#(X,nil()) -> mark#(X) -> mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(X,nil()) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) a____#(X,nil()) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) SCC Processor: #sccs: 1 #rules: 26 #arcs: 147/900 DPs: a__isPal#(V) -> a__isNePal#(V) a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPal(P)) a__and#(tt(),X) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) -> mark#(Z) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isList(X)) -> a__isList#(X) a__isList#(V) -> a__isNeList#(V) a__isNeList#(__(V1,V2)) -> a__isList#(V1) a__isList#(__(V1,V2)) -> a__isList#(V1) a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2)) a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2)) a__isNeList#(__(V1,V2)) -> a__isNeList#(V1) a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2)) mark#(isNeList(X)) -> a__isNeList#(X) mark#(isNePal(X)) -> a__isNePal#(X) mark#(isPal(X)) -> a__isPal#(X) a____#(__(X,Y),Z) -> mark#(Y) a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) -> mark#(X) a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) -> mark#(X) a____#(nil(),X) -> mark#(X) TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) -> a__isQid(V) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isPal(nil()) -> tt() a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=1 interpretation: [a__isPal#](x0) = x0 + 1, [a__isNePal#](x0) = x0, [a__isNeList#](x0) = 2x0, [a__isList#](x0) = 2x0 + 1, [a__and#](x0, x1) = x0 + x1, [mark#](x0) = x0 + 1, [a____#](x0, x1) = 2x0 + x1, [isNePal](x0) = x0, [isQid](x0) = x0, [and](x0, x1) = x0 + x1 + 1, [u] = 2, [o] = 5, [i] = 2, [e] = 4, [a] = 4, [a__isPal](x0) = x0 + 1, [isPal](x0) = x0 + 1, [a__isNePal](x0) = x0, [isNeList](x0) = 2x0, [a__isQid](x0) = x0, [isList](x0) = 2x0 + 1, [a__isNeList](x0) = 2x0, [a__isList](x0) = 2x0 + 1, [a__and](x0, x1) = x0 + x1 + 1, [tt] = 2, [nil] = 4, [mark](x0) = x0, [a____](x0, x1) = 2x0 + x1 + 1, [__](x0, x1) = 2x0 + x1 + 1 orientation: a__isPal#(V) = V + 1 >= V = a__isNePal#(V) a__isNePal#(__(I,__(P,I))) = 3I + 2P + 2 >= I + P + 1 = a__and#(a__isQid(I),isPal(P)) a__and#(tt(),X) = X + 2 >= X + 1 = mark#(X) mark#(__(X1,X2)) = 2X1 + X2 + 2 >= X2 + 1 = mark#(X2) mark#(__(X1,X2)) = 2X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(__(X1,X2)) = 2X1 + X2 + 2 >= 2X1 + X2 = a____#(mark(X1),mark(X2)) a____#(__(X,Y),Z) = 4X + 2Y + Z + 2 >= Z + 1 = mark#(Z) mark#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 = a__and#(mark(X1),X2) mark#(isList(X)) = 2X + 2 >= 2X + 1 = a__isList#(X) a__isList#(V) = 2V + 1 >= 2V = a__isNeList#(V) a__isNeList#(__(V1,V2)) = 4V1 + 2V2 + 2 >= 2V1 + 1 = a__isList#(V1) a__isList#(__(V1,V2)) = 4V1 + 2V2 + 3 >= 2V1 + 1 = a__isList#(V1) a__isList#(__(V1,V2)) = 4V1 + 2V2 + 3 >= 2V1 + 2V2 + 2 = a__and#(a__isList(V1),isList(V2)) a__isNeList#(__(V1,V2)) = 4V1 + 2V2 + 2 >= 2V1 + 2V2 + 1 = a__and#(a__isList(V1),isNeList(V2)) a__isNeList#(__(V1,V2)) = 4V1 + 2V2 + 2 >= 2V1 = a__isNeList#(V1) a__isNeList#(__(V1,V2)) = 4V1 + 2V2 + 2 >= 2V1 + 2V2 + 1 = a__and#(a__isNeList(V1),isList(V2)) mark#(isNeList(X)) = 2X + 1 >= 2X = a__isNeList#(X) mark#(isNePal(X)) = X + 1 >= X = a__isNePal#(X) mark#(isPal(X)) = X + 2 >= X + 1 = a__isPal#(X) a____#(__(X,Y),Z) = 4X + 2Y + Z + 2 >= Y + 1 = mark#(Y) a____#(__(X,Y),Z) = 4X + 2Y + Z + 2 >= 2Y + Z = a____#(mark(Y),mark(Z)) a____#(__(X,Y),Z) = 4X + 2Y + Z + 2 >= X + 1 = mark#(X) a____#(__(X,Y),Z) = 4X + 2Y + Z + 2 >= 2X + 2Y + Z + 1 = a____#(mark(X),a____(mark(Y),mark(Z))) a____#(X,nil()) = 2X + 4 >= X + 1 = mark#(X) a____#(nil(),X) = X + 8 >= X + 1 = mark#(X) a____(__(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 2X + 5 >= X = mark(X) a____(nil(),X) = X + 9 >= X = mark(X) a__and(tt(),X) = X + 3 >= X = mark(X) a__isList(V) = 2V + 1 >= 2V = a__isNeList(V) a__isList(nil()) = 9 >= 2 = tt() a__isList(__(V1,V2)) = 4V1 + 2V2 + 3 >= 2V1 + 2V2 + 3 = a__and(a__isList(V1),isList(V2)) a__isNeList(V) = 2V >= V = a__isQid(V) a__isNeList(__(V1,V2)) = 4V1 + 2V2 + 2 >= 2V1 + 2V2 + 2 = a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) = 4V1 + 2V2 + 2 >= 2V1 + 2V2 + 2 = a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) = V >= V = a__isQid(V) a__isNePal(__(I,__(P,I))) = 3I + 2P + 2 >= I + P + 2 = a__and(a__isQid(I),isPal(P)) a__isPal(V) = V + 1 >= V = a__isNePal(V) a__isPal(nil()) = 5 >= 2 = tt() a__isQid(a()) = 4 >= 2 = tt() a__isQid(e()) = 4 >= 2 = tt() a__isQid(i()) = 2 >= 2 = tt() a__isQid(o()) = 5 >= 2 = tt() a__isQid(u()) = 2 >= 2 = tt() mark(__(X1,X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__and(mark(X1),X2) mark(isList(X)) = 2X + 1 >= 2X + 1 = a__isList(X) mark(isNeList(X)) = 2X >= 2X = a__isNeList(X) mark(isQid(X)) = X >= X = a__isQid(X) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(isPal(X)) = X + 1 >= X + 1 = a__isPal(X) mark(nil()) = 4 >= 4 = nil() mark(tt()) = 2 >= 2 = tt() mark(a()) = 4 >= 4 = a() mark(e()) = 4 >= 4 = e() mark(i()) = 2 >= 2 = i() mark(o()) = 5 >= 5 = o() mark(u()) = 2 >= 2 = u() a____(X1,X2) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2) a__and(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = and(X1,X2) a__isList(X) = 2X + 1 >= 2X + 1 = isList(X) a__isNeList(X) = 2X >= 2X = isNeList(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X >= X = isNePal(X) a__isPal(X) = X + 1 >= X + 1 = isPal(X) problem: DPs: TRS: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) -> mark(X) a____(nil(),X) -> mark(X) a__and(tt(),X) -> mark(X) a__isList(V) -> a__isNeList(V) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2)) a__isNeList(V) -> a__isQid(V) a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2)) a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2)) a__isNePal(V) -> a__isQid(V) a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P)) a__isPal(V) -> a__isNePal(V) a__isPal(nil()) -> tt() a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(isNeList(X)) -> a__isNeList(X) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(isPal(X)) -> a__isPal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isList(X) -> isList(X) a__isNeList(X) -> isNeList(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) a__isPal(X) -> isPal(X) Qed