YES Problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) 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)) U11#(tt(),V) -> activate#(V) U11#(tt(),V) -> isNeList#(activate(V)) U11#(tt(),V) -> U12#(isNeList(activate(V))) U21#(tt(),V1,V2) -> activate#(V2) U21#(tt(),V1,V2) -> activate#(V1) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> activate#(V2) U22#(tt(),V2) -> isList#(activate(V2)) U22#(tt(),V2) -> U23#(isList(activate(V2))) U31#(tt(),V) -> activate#(V) U31#(tt(),V) -> isQid#(activate(V)) U31#(tt(),V) -> U32#(isQid(activate(V))) U41#(tt(),V1,V2) -> activate#(V2) U41#(tt(),V1,V2) -> activate#(V1) U41#(tt(),V1,V2) -> isList#(activate(V1)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> activate#(V2) U42#(tt(),V2) -> isNeList#(activate(V2)) U42#(tt(),V2) -> U43#(isNeList(activate(V2))) U51#(tt(),V1,V2) -> activate#(V2) U51#(tt(),V1,V2) -> activate#(V1) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) U52#(tt(),V2) -> activate#(V2) U52#(tt(),V2) -> isList#(activate(V2)) U52#(tt(),V2) -> U53#(isList(activate(V2))) U61#(tt(),V) -> activate#(V) U61#(tt(),V) -> isQid#(activate(V)) U61#(tt(),V) -> U62#(isQid(activate(V))) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) U71#(tt(),V) -> U72#(isNePal(activate(V))) and#(tt(),X) -> activate#(X) isList#(V) -> activate#(V) isList#(V) -> isPalListKind#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(V) -> activate#(V) isNeList#(V) -> isPalListKind#(activate(V)) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> isPal#(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__isPalListKind(activate(I))) isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and( isPal(activate(P)), n__isPalListKind (activate(P)))) isPal#(V) -> activate#(V) isPal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) isPalListKind#(n____(V1,V2)) -> activate#(V1) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(X1,X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(X1,X2) 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 U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) 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)) U11#(tt(),V) -> activate#(V) U11#(tt(),V) -> isNeList#(activate(V)) U11#(tt(),V) -> U12#(isNeList(activate(V))) U21#(tt(),V1,V2) -> activate#(V2) U21#(tt(),V1,V2) -> activate#(V1) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> activate#(V2) U22#(tt(),V2) -> isList#(activate(V2)) U22#(tt(),V2) -> U23#(isList(activate(V2))) U31#(tt(),V) -> activate#(V) U31#(tt(),V) -> isQid#(activate(V)) U31#(tt(),V) -> U32#(isQid(activate(V))) U41#(tt(),V1,V2) -> activate#(V2) U41#(tt(),V1,V2) -> activate#(V1) U41#(tt(),V1,V2) -> isList#(activate(V1)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> activate#(V2) U42#(tt(),V2) -> isNeList#(activate(V2)) U42#(tt(),V2) -> U43#(isNeList(activate(V2))) U51#(tt(),V1,V2) -> activate#(V2) U51#(tt(),V1,V2) -> activate#(V1) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) U52#(tt(),V2) -> activate#(V2) U52#(tt(),V2) -> isList#(activate(V2)) U52#(tt(),V2) -> U53#(isList(activate(V2))) U61#(tt(),V) -> activate#(V) U61#(tt(),V) -> isQid#(activate(V)) U61#(tt(),V) -> U62#(isQid(activate(V))) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) U71#(tt(),V) -> U72#(isNePal(activate(V))) and#(tt(),X) -> activate#(X) isList#(V) -> activate#(V) isList#(V) -> isPalListKind#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(V) -> activate#(V) isNeList#(V) -> isPalListKind#(activate(V)) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> isPal#(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__isPalListKind(activate(I))) isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal#(V) -> activate#(V) isPal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) isPalListKind#(n____(V1,V2)) -> activate#(V1) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(X1,X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(X1,X2) 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 U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and( isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) 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) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isPal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) -> U71#(tt(),V) -> U72#(isNePal(activate(V))) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) -> U71#(tt(),V) -> isNePal#(activate(V)) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) -> U71#(tt(),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__and(X1,X2)) -> and#(X1,X2) isPal#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__u()) -> u#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__o()) -> o#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__i()) -> i#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__e()) -> e#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__a()) -> a#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() 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__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) and#(tt(),X) -> activate#(X) -> activate#(n____(X1,X2)) -> __#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) -> isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) -> isPal#(V) -> isPalListKind#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) -> isPal#(V) -> activate#(V) isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) -> and#(tt(),X) -> activate#(X) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) -> and#(tt(),X) -> activate#(X) 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__and(X1,X2)) -> and#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__isPalListKind(X)) -> isPalListKind#(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__and(X1,X2)) -> and#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__isPalListKind(X)) -> isPalListKind#(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#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNePal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isNePal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) -> U61#(tt(),V) -> U62#(isQid(activate(V))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) -> U61#(tt(),V) -> isQid#(activate(V)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) -> U61#(tt(),V) -> activate#(V) 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__and(X1,X2)) -> and#(X1,X2) isNePal#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNePal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNePal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(I) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(P) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(V) -> isPalListKind#(activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(V) -> activate#(V) U71#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U71#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U71#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U71#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U71#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U71#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U71#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U71#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U71#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() U61#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U61#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U61#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U61#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U61#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U61#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U61#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U61#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U61#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V1) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V2) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> isPalListKind#(activate(V)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> activate#(V) U52#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U52#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U52#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> U53#(isList(activate(V2))) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> isList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> activate#(V2) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V1) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V2) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(V) -> isPalListKind#(activate(V)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(V) -> activate#(V) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__u()) -> u#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__o()) -> o#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__i()) -> i#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__e()) -> e#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__a()) -> a#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__u()) -> u#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__o()) -> o#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__i()) -> i#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__e()) -> e#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__a()) -> a#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> activate#(V1) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> activate#(V2) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> isPalListKind#(activate(V)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> activate#(V) U42#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U42#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U42#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> U43#(isNeList(activate(V2))) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> isNeList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> activate#(V2) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> isPalListKind#(activate(V)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__u()) -> u#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__o()) -> o#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__i()) -> i#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__e()) -> e#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__a()) -> a#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__u()) -> u#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__o()) -> o#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__i()) -> i#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__e()) -> e#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__a()) -> a#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() U31#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U31#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U31#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U31#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U31#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U31#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U31#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U31#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U31#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V1) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V2) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> isPalListKind#(activate(V)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> activate#(V) U22#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U22#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U22#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U22#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> activate#(V1) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> activate#(V2) 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__and(X1,X2)) -> and#(X1,X2) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(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__and(X1,X2)) -> and#(X1,X2) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) 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__and(X1,X2)) -> and#(X1,X2) isList#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) -> U11#(tt(),V) -> U12#(isNeList(activate(V))) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) -> U11#(tt(),V) -> isNeList#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) -> U11#(tt(),V) -> activate#(V) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) -> U22#(tt(),V2) -> U23#(isList(activate(V2))) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) -> U22#(tt(),V2) -> isList#(activate(V2)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) -> U22#(tt(),V2) -> activate#(V2) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> isPalListKind#(activate(V)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__u()) -> u#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__o()) -> o#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__i()) -> i#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__e()) -> e#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__a()) -> a#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__u()) -> u#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__o()) -> o#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__i()) -> i#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__e()) -> e#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__a()) -> a#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> activate#(V1) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> activate#(V2) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> activate#(V1) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> activate#(V2) 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__and(X1,X2)) -> and#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(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__and(X1,X2)) -> and#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> U32#(isQid(activate(V))) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> isQid#(activate(V)) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> activate#(V) 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__and(X1,X2)) -> and#(X1,X2) isNeList#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() activate#(n__and(X1,X2)) -> and#(X1,X2) -> and#(tt(),X) -> activate#(X) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(Y,Z) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V1) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V2) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(V) -> isPalListKind#(activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(V) -> activate#(V) U11#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U11#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U11#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U11#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U11#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U11#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U11#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U11#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U11#(tt(),V) -> activate#(V) -> 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: 4 #rules: 26 #arcs: 382/6084 DPs: U52#(tt(),V2) -> isList#(activate(V2)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Usable Rule Processor: DPs: U52#(tt(),V2) -> isList#(activate(V2)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() KBO Processor: argument filtering: pi(__) = [0,1] pi(nil) = [] pi(tt) = [] pi(U11) = [] pi(activate) = [0] pi(isNeList) = 0 pi(U12) = [] pi(U21) = 2 pi(isList) = 0 pi(U22) = [] pi(U23) = [] pi(U31) = [] pi(isQid) = [] pi(U32) = 0 pi(U41) = 0 pi(U42) = [] pi(U43) = 0 pi(U51) = 2 pi(U52) = [0] pi(U53) = [] pi(and) = [0,1] pi(isPalListKind) = 0 pi(n__nil) = [] pi(n____) = [0,1] pi(n__isPalListKind) = 0 pi(n__and) = [0,1] pi(n__a) = [] pi(n__e) = [] pi(n__i) = [] pi(n__o) = [] pi(n__u) = [] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(U11#) = [1] pi(isNeList#) = 0 pi(U21#) = [1,2] pi(isList#) = [0] pi(U22#) = [1] pi(U41#) = [1,2] pi(U42#) = [1] pi(U51#) = [1,2] pi(U52#) = [1] usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() weight function: w0 = 1 w(U52#) = w(U42#) = w(U22#) = w(isList#) = w(U21#) = w(U11#) = w( u) = w(o) = w(i) = w(e) = w(a) = w(n__u) = w(n__o) = w(n__i) = w( n__e) = w(n__a) = w(n____) = w(n__nil) = w(U53) = w(U52) = w(U51) = w( U42) = w(U41) = w(U32) = w(isQid) = w(U31) = w(U23) = w(U22) = w( isList) = w(U21) = w(U12) = w(U11) = w(tt) = w(nil) = w(__) = 1 w(U51#) = w(U41#) = w(isNeList#) = w(n__and) = w(n__isPalListKind) = w( isPalListKind) = w(and) = w(U43) = w(isNeList) = w(activate) = 0 precedence: U51# ~ U41# ~ U22# ~ U21# ~ U53 ~ U52 ~ U42 ~ isQid ~ U31 ~ U23 ~ U22 ~ U12 ~ activate ~ U11 > U52# ~ u ~ o ~ i ~ e ~ a ~ nil ~ __ > isList# ~ n__u ~ n__o ~ n__i ~ n__e ~ n__a ~ n__nil ~ and > U42# ~ isNeList# ~ U11# ~ n__and ~ n__isPalListKind ~ n____ ~ isPalListKind ~ U51 ~ U43 ~ U41 ~ U32 ~ isList ~ U21 ~ isNeList ~ tt problem: DPs: TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() Qed DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Usable Rule Processor: DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Arctic Interpretation Processor: dimension: 1 usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() interpretation: [isPal#](x0) = 1x0 + 1, [isNePal#](x0) = x0 + 0, [U71#](x0, x1) = x0 + x1 + 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [n__u] = 0, [n__o] = 0, [n__i] = 0, [n__e] = 0, [n__a] = 0, [n__and](x0, x1) = x0 + x1, [n__isPalListKind](x0) = x0, [n____](x0, x1) = 1x0 + x1 + 1, [n__nil] = 0, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1 + 0, [activate](x0) = x0 + 0, [tt] = 0, [nil] = 0, [__](x0, x1) = 1x0 + x1 + 1 orientation: isPal#(V) = 1V + 1 >= V + 0 = U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) = V + 0 >= V + 0 = isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) = 1I + 1P + 1 >= 1P + 1 = isPal#(activate(P)) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 1X1 + X2 + 1 >= 1X1 + X2 + 1 = __(X1,X2) activate(n__isPalListKind(X)) = X + 0 >= X = isPalListKind(X) activate(n__and(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X + 0 >= X = X nil() = 0 >= 0 = n__nil() __(__(X,Y),Z) = 2X + 1Y + Z + 2 >= 1X + 1Y + Z + 1 = __(X,__(Y,Z)) __(X,nil()) = 1X + 1 >= X = X __(nil(),X) = X + 1 >= X = X __(X1,X2) = 1X1 + X2 + 1 >= 1X1 + X2 + 1 = n____(X1,X2) isPalListKind(n__a()) = 0 >= 0 = tt() isPalListKind(n__e()) = 0 >= 0 = tt() isPalListKind(n__i()) = 0 >= 0 = tt() isPalListKind(n__nil()) = 0 >= 0 = tt() isPalListKind(n__o()) = 0 >= 0 = tt() isPalListKind(n__u()) = 0 >= 0 = tt() isPalListKind(n____(V1,V2)) = 1V1 + V2 + 1 >= V1 + V2 + 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = X >= X = n__isPalListKind(X) and(tt(),X) = X + 0 >= X + 0 = activate(X) and(X1,X2) = X1 + X2 + 0 >= X1 + X2 = n__and(X1,X2) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() problem: DPs: U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Restore Modifier: DPs: U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) 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: 3/4 DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Usable Rule Processor: DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Semantic Labeling Processor: dimension: 1 usable rules: interpretation: [u] = 2, [o] = 1, [i] = 1, [e] = 2, [a] = 2, [n__u] = 2, [n__o] = 1, [n__i] = 1, [n__e] = 2, [n__a] = 2, [n__and](x0, x1) = x0 + x1, [n__isPalListKind](x0) = x0, [n____](x0, x1) = x0 + x1 + 1, [n__nil] = 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1, [activate](x0) = x0, [tt] = 1, [nil] = 1, [__](x0, x1) = x0 + x1 + 1 labeled: isPalListKind# activate# and# usable (for model): isPalListKind# n____ activate# n__isPalListKind n__and and# tt activate isPalListKind n__nil nil __ and n__a a n__e e n__i i n__o o n__u u argument filtering: pi(__) = 1 pi(nil) = [] pi(tt) = [] pi(activate) = [] pi(and) = 0 pi(isPalListKind) = 0 pi(n__nil) = [] pi(n____) = 0 pi(n__isPalListKind) = [] pi(n__and) = 1 pi(n__a) = [] pi(n__e) = [] pi(n__i) = [] pi(n__o) = [] pi(n__u) = [] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(activate#) = [] pi(and#) = [] pi(isPalListKind#) = [] precedence: isPalListKind# > and# > activate# ~ u ~ o ~ i ~ e ~ a ~ n__u ~ n__o ~ n__i ~ n__e ~ n__a ~ n__and ~ n__isPalListKind ~ n____ ~ n__nil ~ isPalListKind ~ and ~ activate ~ tt ~ nil ~ __ problem: DPs: TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Qed 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 U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) 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 U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) 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) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Qed