YES Problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Proof: DP Processor: DPs: __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) and#(tt(),X) -> activate#(X) isList#(V) -> activate#(V) isList#(V) -> isNeList#(activate(V)) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) isNeList#(V) -> activate#(V) isNeList#(V) -> isQid#(activate(V)) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isNePal#(V) -> activate#(V) isNePal#(V) -> isQid#(activate(V)) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> activate#(I) isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P))) isPal#(V) -> activate#(V) isPal#(V) -> isNePal#(activate(V)) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(X1,X2) activate#(n__isList(X)) -> isList#(X) activate#(n__isNeList(X)) -> isNeList#(X) activate#(n__isPal(X)) -> isPal#(X) activate#(n__a()) -> a#() activate#(n__e()) -> e#() activate#(n__i()) -> i#() activate#(n__o()) -> o#() activate#(n__u()) -> u#() TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X TDG Processor: DPs: __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) and#(tt(),X) -> activate#(X) isList#(V) -> activate#(V) isList#(V) -> isNeList#(activate(V)) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) isNeList#(V) -> activate#(V) isNeList#(V) -> isQid#(activate(V)) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isNePal#(V) -> activate#(V) isNePal#(V) -> isQid#(activate(V)) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> activate#(I) isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P))) isPal#(V) -> activate#(V) isPal#(V) -> isNePal#(activate(V)) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(X1,X2) activate#(n__isList(X)) -> isList#(X) activate#(n__isNeList(X)) -> isNeList#(X) activate#(n__isPal(X)) -> isPal#(X) activate#(n__a()) -> a#() activate#(n__e()) -> e#() activate#(n__i()) -> i#() activate#(n__o()) -> o#() activate#(n__u()) -> u#() TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X graph: isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P))) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(I) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(P) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(V) -> isQid#(activate(V)) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(V) -> activate#(V) isPal#(V) -> activate#(V) -> activate#(n__u()) -> u#() isPal#(V) -> activate#(V) -> activate#(n__o()) -> o#() isPal#(V) -> activate#(V) -> activate#(n__i()) -> i#() isPal#(V) -> activate#(V) -> activate#(n__e()) -> e#() isPal#(V) -> activate#(V) -> activate#(n__a()) -> a#() isPal#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) -> activate#(n__isNeList(X)) -> isNeList#(X) isPal#(V) -> activate#(V) -> activate#(n__isList(X)) -> isList#(X) isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__u()) -> u#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__o()) -> o#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__i()) -> i#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__e()) -> e#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__a()) -> a#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__isPal(X)) -> isPal#(X) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__isNeList(X)) -> isNeList#(X) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__isList(X)) -> isList#(X) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__u()) -> u#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__o()) -> o#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__i()) -> i#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__e()) -> e#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__a()) -> a#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__isPal(X)) -> isPal#(X) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__isNeList(X)) -> isNeList#(X) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__isList(X)) -> isList#(X) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P))) -> and#(tt(),X) -> activate#(X) isNePal#(V) -> activate#(V) -> activate#(n__u()) -> u#() isNePal#(V) -> activate#(V) -> activate#(n__o()) -> o#() isNePal#(V) -> activate#(V) -> activate#(n__i()) -> i#() isNePal#(V) -> activate#(V) -> activate#(n__e()) -> e#() isNePal#(V) -> activate#(V) -> activate#(n__a()) -> a#() isNePal#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X) isNePal#(V) -> activate#(V) -> activate#(n__isNeList(X)) -> isNeList#(X) isNePal#(V) -> activate#(V) -> activate#(n__isList(X)) -> isList#(X) isNePal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNePal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(V) -> isQid#(activate(V)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(V) -> activate#(V) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPal(X)) -> isPal#(X) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isList(X)) -> isList#(X) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__u()) -> u#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__o()) -> o#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__i()) -> i#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__e()) -> e#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__a()) -> a#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPal(X)) -> isPal#(X) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isList(X)) -> isList#(X) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) -> and#(tt(),X) -> activate#(X) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) -> and#(tt(),X) -> activate#(X) isNeList#(V) -> activate#(V) -> activate#(n__u()) -> u#() isNeList#(V) -> activate#(V) -> activate#(n__o()) -> o#() isNeList#(V) -> activate#(V) -> activate#(n__i()) -> i#() isNeList#(V) -> activate#(V) -> activate#(n__e()) -> e#() isNeList#(V) -> activate#(V) -> activate#(n__a()) -> a#() isNeList#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X) isNeList#(V) -> activate#(V) -> activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(V) -> activate#(V) -> activate#(n__isList(X)) -> isList#(X) isNeList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> isNeList#(activate(V)) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPal(X)) -> isPal#(X) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isNeList(X)) -> isNeList#(X) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isList(X)) -> isList#(X) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__u()) -> u#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__o()) -> o#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__i()) -> i#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__e()) -> e#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__a()) -> a#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPal(X)) -> isPal#(X) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isNeList(X)) -> isNeList#(X) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isList(X)) -> isList#(X) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) -> and#(tt(),X) -> activate#(X) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V1) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V2) isList#(V) -> isNeList#(activate(V)) -> isNeList#(V) -> isQid#(activate(V)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(V) -> activate#(V) isList#(V) -> activate#(V) -> activate#(n__u()) -> u#() isList#(V) -> activate#(V) -> activate#(n__o()) -> o#() isList#(V) -> activate#(V) -> activate#(n__i()) -> i#() isList#(V) -> activate#(V) -> activate#(n__e()) -> e#() isList#(V) -> activate#(V) -> activate#(n__a()) -> a#() isList#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X) isList#(V) -> activate#(V) -> activate#(n__isNeList(X)) -> isNeList#(X) isList#(V) -> activate#(V) -> activate#(n__isList(X)) -> isList#(X) isList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() activate#(n__isPal(X)) -> isPal#(X) -> isPal#(V) -> isNePal#(activate(V)) activate#(n__isPal(X)) -> isPal#(X) -> isPal#(V) -> activate#(V) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(n____(V1,V2)) -> isList#(activate(V1)) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(n____(V1,V2)) -> activate#(V1) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(n____(V1,V2)) -> activate#(V2) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(V) -> isQid#(activate(V)) activate#(n__isNeList(X)) -> isNeList#(X) -> isNeList#(V) -> activate#(V) activate#(n__isList(X)) -> isList#(X) -> isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) activate#(n__isList(X)) -> isList#(X) -> isList#(n____(V1,V2)) -> isList#(activate(V1)) activate#(n__isList(X)) -> isList#(X) -> isList#(n____(V1,V2)) -> activate#(V1) activate#(n__isList(X)) -> isList#(X) -> isList#(n____(V1,V2)) -> activate#(V2) activate#(n__isList(X)) -> isList#(X) -> isList#(V) -> isNeList#(activate(V)) activate#(n__isList(X)) -> isList#(X) -> isList#(V) -> activate#(V) activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(Y,Z) and#(tt(),X) -> activate#(X) -> activate#(n__u()) -> u#() and#(tt(),X) -> activate#(X) -> activate#(n__o()) -> o#() and#(tt(),X) -> activate#(X) -> activate#(n__i()) -> i#() and#(tt(),X) -> activate#(X) -> activate#(n__e()) -> e#() and#(tt(),X) -> activate#(X) -> activate#(n__a()) -> a#() and#(tt(),X) -> activate#(X) -> activate#(n__isPal(X)) -> isPal#(X) and#(tt(),X) -> activate#(X) -> activate#(n__isNeList(X)) -> isNeList#(X) and#(tt(),X) -> activate#(X) -> activate#(n__isList(X)) -> isList#(X) and#(tt(),X) -> activate#(X) -> activate#(n____(X1,X2)) -> __#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__nil()) -> nil#() __#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) -> __#(__(X,Y),Z) -> __#(Y,Z) SCC Processor: #sccs: 2 #rules: 25 #arcs: 170/1225 DPs: isPal#(V) -> isNePal#(activate(V)) isNePal#(V) -> activate#(V) activate#(n__isList(X)) -> isList#(X) isList#(V) -> activate#(V) activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(V) -> activate#(V) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) and#(tt(),X) -> activate#(X) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> activate#(I) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P))) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Arctic Interpretation Processor: dimension: 1 interpretation: [isPal#](x0) = 4x0, [isNePal#](x0) = 4x0, [isNeList#](x0) = x0, [isList#](x0) = x0, [activate#](x0) = x0, [and#](x0, x1) = x1, [u] = 4, [o] = 0, [i] = 0, [e] = 0, [a] = 5, [n__u] = 4, [n__o] = 0, [n__i] = 0, [n__e] = 0, [n__a] = 5, [isPal](x0) = 5x0 + 4, [n__isPal](x0) = 5x0 + 4, [isNePal](x0) = 5x0 + 0, [n__isNeList](x0) = x0, [isQid](x0) = x0, [n__isList](x0) = x0, [n____](x0, x1) = 1x0 + x1 + 0, [n__nil] = 0, [isNeList](x0) = x0, [isList](x0) = x0, [activate](x0) = x0, [and](x0, x1) = 1x0 + x1 + 0, [tt] = 0, [nil] = 0, [__](x0, x1) = 1x0 + x1 + 0 orientation: isPal#(V) = 4V >= 4V = isNePal#(activate(V)) isNePal#(V) = 4V >= V = activate#(V) activate#(n__isList(X)) = X >= X = isList#(X) isList#(V) = V >= V = activate#(V) activate#(n__isNeList(X)) = X >= X = isNeList#(X) isNeList#(V) = V >= V = activate#(V) activate#(n__isPal(X)) = 5X + 4 >= 4X = isPal#(X) isPal#(V) = 4V >= V = activate#(V) isNeList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V2 = activate#(V2) isNeList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V1 = activate#(V1) isNeList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V1 = isList#(activate(V1)) isList#(V) = V >= V = isNeList#(activate(V)) isNeList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V2 = and#(isList(activate(V1)),n__isNeList(activate(V2))) and#(tt(),X) = X >= X = activate#(X) isNeList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V1 = isNeList#(activate(V1)) isNeList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V2 = and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V2 = activate#(V2) isList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V1 = activate#(V1) isList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V1 = isList#(activate(V1)) isList#(n____(V1,V2)) = 1V1 + V2 + 0 >= V2 = and#(isList(activate(V1)),n__isList(activate(V2))) isNePal#(n____(I,__(P,I))) = 5I + 5P + 4 >= P = activate#(P) isNePal#(n____(I,__(P,I))) = 5I + 5P + 4 >= I = activate#(I) isNePal#(n____(I,__(P,I))) = 5I + 5P + 4 >= 5P + 4 = and#(isQid(activate(I)),n__isPal(activate(P))) __(__(X,Y),Z) = 2X + 1Y + Z + 1 >= 1X + 1Y + Z + 0 = __(X,__(Y,Z)) __(X,nil()) = 1X + 0 >= X = X __(nil(),X) = X + 1 >= X = X and(tt(),X) = X + 1 >= X = activate(X) isList(V) = V >= V = isNeList(activate(V)) isList(n__nil()) = 0 >= 0 = tt() isList(n____(V1,V2)) = 1V1 + V2 + 0 >= 1V1 + V2 + 0 = and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) = V >= V = isQid(activate(V)) isNeList(n____(V1,V2)) = 1V1 + V2 + 0 >= 1V1 + V2 + 0 = and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) = 1V1 + V2 + 0 >= 1V1 + V2 + 0 = and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) = 5V + 0 >= V = isQid(activate(V)) isNePal(n____(I,__(P,I))) = 6I + 6P + 5 >= 1I + 5P + 4 = and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) = 5V + 4 >= 5V + 0 = isNePal(activate(V)) isPal(n__nil()) = 5 >= 0 = tt() isQid(n__a()) = 5 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 0 >= 0 = tt() isQid(n__o()) = 0 >= 0 = tt() isQid(n__u()) = 4 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = n____(X1,X2) isList(X) = X >= X = n__isList(X) isNeList(X) = X >= X = n__isNeList(X) isPal(X) = 5X + 4 >= 5X + 4 = n__isPal(X) a() = 5 >= 5 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 4 >= 4 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = __(X1,X2) activate(n__isList(X)) = X >= X = isList(X) activate(n__isNeList(X)) = X >= X = isNeList(X) activate(n__isPal(X)) = 5X + 4 >= 5X + 4 = isPal(X) activate(n__a()) = 5 >= 5 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 4 >= 4 = u() activate(X) = X >= X = X problem: DPs: isPal#(V) -> isNePal#(activate(V)) activate#(n__isList(X)) -> isList#(X) isList#(V) -> activate#(V) activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(V) -> activate#(V) isNeList#(n____(V1,V2)) -> activate#(V2) isList#(V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) and#(tt(),X) -> activate#(X) isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P))) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X SCC Processor: #sccs: 1 #rules: 11 #arcs: 82/169 DPs: and#(tt(),X) -> activate#(X) activate#(n__isList(X)) -> isList#(X) isList#(V) -> activate#(V) activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(V) -> activate#(V) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(V) -> isNeList#(activate(V)) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Arctic Interpretation Processor: dimension: 1 interpretation: [isNeList#](x0) = 1x0, [isList#](x0) = 1x0, [activate#](x0) = x0, [and#](x0, x1) = 1x0 + x1, [u] = 5, [o] = 5, [i] = 1, [e] = 6, [a] = 2, [n__u] = 5, [n__o] = 5, [n__i] = 1, [n__e] = 6, [n__a] = 2, [isPal](x0) = 2x0, [n__isPal](x0) = 2x0, [isNePal](x0) = x0, [n__isNeList](x0) = 1x0, [isQid](x0) = x0, [n__isList](x0) = 1x0 + -8, [n____](x0, x1) = 2x0 + x1 + -1, [n__nil] = 0, [isNeList](x0) = 1x0, [isList](x0) = 1x0 + -8, [activate](x0) = x0, [and](x0, x1) = 2x0 + x1, [tt] = 0, [nil] = 0, [__](x0, x1) = 2x0 + x1 + -1 orientation: and#(tt(),X) = X + 1 >= X = activate#(X) activate#(n__isList(X)) = 1X + -8 >= 1X = isList#(X) isList#(V) = 1V >= V = activate#(V) activate#(n__isNeList(X)) = 1X >= 1X = isNeList#(X) isNeList#(V) = 1V >= V = activate#(V) isNeList#(n____(V1,V2)) = 3V1 + 1V2 + 0 >= V2 = activate#(V2) isNeList#(n____(V1,V2)) = 3V1 + 1V2 + 0 >= 2V1 + 1V2 + -7 = and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) = 3V1 + 1V2 + 0 >= 2V1 + 1V2 + -8 = and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(V) = 1V >= 1V = isNeList#(activate(V)) isList#(n____(V1,V2)) = 3V1 + 1V2 + 0 >= V2 = activate#(V2) isList#(n____(V1,V2)) = 3V1 + 1V2 + 0 >= 2V1 + 1V2 + -7 = and#(isList(activate(V1)),n__isList(activate(V2))) __(__(X,Y),Z) = 4X + 2Y + Z + 1 >= 2X + 2Y + Z + -1 = __(X,__(Y,Z)) __(X,nil()) = 2X + 0 >= X = X __(nil(),X) = X + 2 >= X = X and(tt(),X) = X + 2 >= X = activate(X) isList(V) = 1V + -8 >= 1V = isNeList(activate(V)) isList(n__nil()) = 1 >= 0 = tt() isList(n____(V1,V2)) = 3V1 + 1V2 + 0 >= 3V1 + 1V2 + -6 = and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) = 1V >= V = isQid(activate(V)) isNeList(n____(V1,V2)) = 3V1 + 1V2 + 0 >= 3V1 + 1V2 + -6 = and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) = 3V1 + 1V2 + 0 >= 3V1 + 1V2 + -8 = and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) = V >= V = isQid(activate(V)) isNePal(n____(I,__(P,I))) = 2I + 2P + -1 >= 2I + 2P = and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) = 2V >= V = isNePal(activate(V)) isPal(n__nil()) = 2 >= 0 = tt() isQid(n__a()) = 2 >= 0 = tt() isQid(n__e()) = 6 >= 0 = tt() isQid(n__i()) = 1 >= 0 = tt() isQid(n__o()) = 5 >= 0 = tt() isQid(n__u()) = 5 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = 2X1 + X2 + -1 >= 2X1 + X2 + -1 = n____(X1,X2) isList(X) = 1X + -8 >= 1X + -8 = n__isList(X) isNeList(X) = 1X >= 1X = n__isNeList(X) isPal(X) = 2X >= 2X = n__isPal(X) a() = 2 >= 2 = n__a() e() = 6 >= 6 = n__e() i() = 1 >= 1 = n__i() o() = 5 >= 5 = n__o() u() = 5 >= 5 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 2X1 + X2 + -1 >= 2X1 + X2 + -1 = __(X1,X2) activate(n__isList(X)) = 1X + -8 >= 1X + -8 = isList(X) activate(n__isNeList(X)) = 1X >= 1X = isNeList(X) activate(n__isPal(X)) = 2X >= 2X = isPal(X) activate(n__a()) = 2 >= 2 = a() activate(n__e()) = 6 >= 6 = e() activate(n__i()) = 1 >= 1 = i() activate(n__o()) = 5 >= 5 = o() activate(n__u()) = 5 >= 5 = u() activate(X) = X >= X = X problem: DPs: and#(tt(),X) -> activate#(X) activate#(n__isList(X)) -> isList#(X) activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(V) -> isNeList#(activate(V)) isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [isNeList#](x0) = 2x0, [isList#](x0) = 2x0, [activate#](x0) = x0, [and#](x0, x1) = 2x0 + x1, [u] = 2, [o] = 4, [i] = 4, [e] = 1, [a] = 1, [n__u] = 2, [n__o] = 4, [n__i] = 4, [n__e] = 1, [n__a] = 1, [isPal](x0) = 3x0, [n__isPal](x0) = 3x0, [isNePal](x0) = 3x0, [n__isNeList](x0) = 2x0, [isQid](x0) = 2x0, [n__isList](x0) = 2x0, [n____](x0, x1) = 3x0 + x1, [n__nil] = 1, [isNeList](x0) = 2x0, [isList](x0) = 2x0, [activate](x0) = x0, [and](x0, x1) = x1, [tt] = 2, [nil] = 1, [__](x0, x1) = 3x0 + x1 orientation: and#(tt(),X) = X + 4 >= X = activate#(X) activate#(n__isList(X)) = 2X >= 2X = isList#(X) activate#(n__isNeList(X)) = 2X >= 2X = isNeList#(X) isNeList#(n____(V1,V2)) = 6V1 + 2V2 >= 4V1 + 2V2 = and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) = 6V1 + 2V2 >= 4V1 + 2V2 = and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(V) = 2V >= 2V = isNeList#(activate(V)) isList#(n____(V1,V2)) = 6V1 + 2V2 >= 4V1 + 2V2 = and#(isList(activate(V1)),n__isList(activate(V2))) __(__(X,Y),Z) = 9X + 3Y + Z >= 3X + 3Y + Z = __(X,__(Y,Z)) __(X,nil()) = 3X + 1 >= X = X __(nil(),X) = X + 3 >= X = X and(tt(),X) = X >= X = activate(X) isList(V) = 2V >= 2V = isNeList(activate(V)) isList(n__nil()) = 2 >= 2 = tt() isList(n____(V1,V2)) = 6V1 + 2V2 >= 2V2 = and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) = 2V >= 2V = isQid(activate(V)) isNeList(n____(V1,V2)) = 6V1 + 2V2 >= 2V2 = and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) = 6V1 + 2V2 >= 2V2 = and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) = 3V >= 2V = isQid(activate(V)) isNePal(n____(I,__(P,I))) = 12I + 9P >= 3P = and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) = 3V >= 3V = isNePal(activate(V)) isPal(n__nil()) = 3 >= 2 = tt() isQid(n__a()) = 2 >= 2 = tt() isQid(n__e()) = 2 >= 2 = tt() isQid(n__i()) = 8 >= 2 = tt() isQid(n__o()) = 8 >= 2 = tt() isQid(n__u()) = 4 >= 2 = tt() nil() = 1 >= 1 = n__nil() __(X1,X2) = 3X1 + X2 >= 3X1 + X2 = n____(X1,X2) isList(X) = 2X >= 2X = n__isList(X) isNeList(X) = 2X >= 2X = n__isNeList(X) isPal(X) = 3X >= 3X = n__isPal(X) a() = 1 >= 1 = n__a() e() = 1 >= 1 = n__e() i() = 4 >= 4 = n__i() o() = 4 >= 4 = n__o() u() = 2 >= 2 = n__u() activate(n__nil()) = 1 >= 1 = nil() activate(n____(X1,X2)) = 3X1 + X2 >= 3X1 + X2 = __(X1,X2) activate(n__isList(X)) = 2X >= 2X = isList(X) activate(n__isNeList(X)) = 2X >= 2X = isNeList(X) activate(n__isPal(X)) = 3X >= 3X = isPal(X) activate(n__a()) = 1 >= 1 = a() activate(n__e()) = 1 >= 1 = e() activate(n__i()) = 4 >= 4 = i() activate(n__o()) = 4 >= 4 = o() activate(n__u()) = 2 >= 2 = u() activate(X) = X >= X = X problem: DPs: activate#(n__isList(X)) -> isList#(X) activate#(n__isNeList(X)) -> isNeList#(X) isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) isList#(V) -> isNeList#(activate(V)) isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X SCC Processor: #sccs: 0 #rules: 0 #arcs: 25/36 DPs: __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Subterm Criterion Processor: simple projection: pi(__#) = 0 problem: DPs: TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Qed