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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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)) 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,n____(P,I))) -> activate#(P) isNePal#(n____(I,n____(P,I))) -> activate#(I) isNePal#(n____(I,n____(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and( n__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)) -> activate#(X2) activate#(n____(X1,X2)) -> activate#(X1) activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) 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 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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)) 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,n____(P,I))) -> activate#(P) isNePal#(n____(I,n____(P,I))) -> activate#(I) isNePal#(n____(I,n____(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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)) -> activate#(X2) activate#(n____(X1,X2)) -> activate#(X1) activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) 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 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and( n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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) -> 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__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isPal#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) isPal#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(X1) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) and#(tt(),X) -> activate#(X) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) -> activate#(n__and(X1,X2)) -> activate#(X1) and#(tt(),X) -> activate#(X) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) and#(tt(),X) -> activate#(X) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) and#(tt(),X) -> activate#(X) -> activate#(n____(X1,X2)) -> activate#(X1) and#(tt(),X) -> activate#(X) -> activate#(n____(X1,X2)) -> activate#(X2) and#(tt(),X) -> activate#(X) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (activate(P)))) -> and#(tt(),X) -> activate#(X) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) -> and#(tt(),X) -> activate#(X) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__u()) -> u#() isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__o()) -> o#() isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__i()) -> i#() isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__e()) -> e#() isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__a()) -> a#() isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__isPal(X)) -> isPal#(X) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__and(X1,X2)) -> activate#(X1) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n____(X1,X2)) -> activate#(X1) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n____(X1,X2)) -> activate#(X2) isNePal#(n____(I,n____(P,I))) -> activate#(P) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__u()) -> u#() isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__o()) -> o#() isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__i()) -> i#() isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__e()) -> e#() isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__a()) -> a#() isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__isPal(X)) -> isPal#(X) isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__and(X1,X2)) -> activate#(X1) isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n____(X1,X2)) -> activate#(X1) isNePal#(n____(I,n____(P,I))) -> activate#(I) -> activate#(n____(X1,X2)) -> activate#(X2) isNePal#(n____(I,n____(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__isPal(X)) -> isPal#(X) isNePal#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNePal#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) isNePal#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNePal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isNePal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) isNePal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X2) isNePal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (activate(P)))) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,n____(P,I))) -> isQid#(activate(I)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,n____(P,I))) -> activate#(I) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,n____(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__isPal(X)) -> isPal#(X) U71#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U71#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) U71#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U71#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U71#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) U71#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U61#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U61#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) U61#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U61#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U61#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) U61#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U52#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U52#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U52#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) U52#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U42#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U42#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U42#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) U42#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U31#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U31#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) U31#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U31#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U31#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) U31#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U22#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U22#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U22#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U22#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U22#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) U22#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__and(X1,X2)) -> and#(activate(X1),X2) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(X1) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) isList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) isList#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) isList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(X1) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(X1) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> activate#(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__and(X1,X2)) -> and#(activate(X1),X2) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(X1) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> activate#(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__isPal(X)) -> isPal#(X) isNeList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNeList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) isNeList#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) isNeList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) isNeList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X2) isNeList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() activate#(n__and(X1,X2)) -> and#(activate(X1),X2) -> and#(tt(),X) -> activate#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__u()) -> u#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__o()) -> o#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__i()) -> i#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__e()) -> e#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__a()) -> a#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__isPal(X)) -> isPal#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n____(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n____(X1,X2)) -> activate#(X2) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__nil()) -> nil#() activate#(n__isPal(X)) -> isPal#(X) -> isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) activate#(n__isPal(X)) -> isPal#(X) -> isPal#(V) -> isPalListKind#(activate(V)) activate#(n__isPal(X)) -> isPal#(X) -> isPal#(V) -> activate#(V) 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)) -> activate#(X2) -> activate#(n__u()) -> u#() activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__o()) -> o#() activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__i()) -> i#() activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__e()) -> e#() activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__a()) -> a#() activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__isPal(X)) -> isPal#(X) activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__and(X1,X2)) -> activate#(X1) activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n____(X1,X2)) -> activate#(X1) activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n____(X1,X2)) -> activate#(X2) activate#(n____(X1,X2)) -> activate#(X2) -> activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__u()) -> u#() activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__o()) -> o#() activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__i()) -> i#() activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__e()) -> e#() activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__a()) -> a#() activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__isPal(X)) -> isPal#(X) activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> activate#(X1) activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n____(X1,X2)) -> activate#(X1) activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n____(X1,X2)) -> activate#(X2) activate#(n____(X1,X2)) -> activate#(X1) -> activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) activate#(n____(X1,X2)) -> __#(activate(X1),activate(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__isPal(X)) -> isPal#(X) U11#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U11#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) U11#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U11#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) U11#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1) U11#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(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: 3 #rules: 40 #arcs: 524/6561 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 usable rules: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X 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() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) 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)) 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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 interpretation: [U52](x0, x1) = x0, [U22#](x0, x1) = 2x1 + 6, [activate](x0) = x0, [U42](x0, x1) = x1 + 0, [isList](x0) = 2x0 + 0, [nil] = 0, [U11](x0, x1) = x0 + 1x1 + 0, [U43](x0) = 0, [U62](x0) = 0, [n__o] = 5, [isPalListKind](x0) = 0, [isPal](x0) = 4, [U53](x0) = 0, [U51](x0, x1, x2) = 5x0 + x1 + 0, [n__nil] = 0, [n__e] = 0, [U71](x0, x1) = 2x0 + 0, [n____](x0, x1) = 2x0 + x1 + 5, [U11#](x0, x1) = x0 + 2x1 + 0, [isNeList](x0) = x0, [n__a] = 0, [U23](x0) = 0, [__](x0, x1) = 2x0 + x1 + 5, [e] = 0, [U21](x0, x1, x2) = 2x1 + 1x2 + 0, [U61](x0, x1) = 2x1, [and](x0, x1) = x0 + x1 + 0, [isList#](x0) = 2x0 + 0, [n__isPal](x0) = 4, [U41](x0, x1, x2) = x1 + x2 + 0, [U42#](x0, x1) = 2x1 + 4, [n__and](x0, x1) = x0 + x1 + 0, [isQid](x0) = x0, [isNePal](x0) = 0, [U72](x0) = 2, [U31](x0, x1) = x1, [U22](x0, x1) = 5x0 + 8, [U32](x0) = x0, [i] = 4, [U41#](x0, x1, x2) = 7x0 + 2x1 + 2x2 + 0, [U52#](x0, x1) = 4x0 + 2x1, [U12](x0) = 8, [a] = 0, [U51#](x0, x1, x2) = x0 + 4x1 + 2x2 + 0, [U21#](x0, x1, x2) = 7x0 + 2x1 + 2x2 + 0, [n__u] = 0, [o] = 5, [u] = 0, [isNeList#](x0) = 2x0, [n__i] = 4, [n__isPalListKind](x0) = 0, [tt] = 0 orientation: U52#(tt(),V2) = 2V2 + 4 >= 2V2 + 0 = isList#(activate(V2)) isList#(V) = 2V + 0 >= 2V + 0 = U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) = 2V + 0 >= 2V = isNeList#(activate(V)) isNeList#(n____(V1,V2)) = 4V1 + 2V2 + 7 >= 2V1 + 2V2 + 7 = U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U41#(tt(),V1,V2) = 2V1 + 2V2 + 7 >= 2V1 + 0 = isList#(activate(V1)) isList#(n____(V1,V2)) = 4V1 + 2V2 + 7 >= 2V1 + 2V2 + 7 = U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U21#(tt(),V1,V2) = 2V1 + 2V2 + 7 >= 2V1 + 0 = isList#(activate(V1)) U21#(tt(),V1,V2) = 2V1 + 2V2 + 7 >= 2V2 + 6 = U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) = 2V2 + 6 >= 2V2 + 0 = isList#(activate(V2)) U41#(tt(),V1,V2) = 2V1 + 2V2 + 7 >= 2V2 + 4 = U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) = 2V2 + 4 >= 2V2 = isNeList#(activate(V2)) isNeList#(n____(V1,V2)) = 4V1 + 2V2 + 7 >= 4V1 + 2V2 + 0 = U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U51#(tt(),V1,V2) = 4V1 + 2V2 + 0 >= 2V1 = isNeList#(activate(V1)) U51#(tt(),V1,V2) = 4V1 + 2V2 + 0 >= 4V1 + 2V2 = U52#(isNeList(activate(V1)),activate(V2)) __(__(X,Y),Z) = 4X + 2Y + Z + 7 >= 2X + 2Y + Z + 5 = __(X,__(Y,Z)) __(X,nil()) = 2X + 5 >= X = X __(nil(),X) = X + 5 >= X = X U11(tt(),V) = 1V + 0 >= 8 = U12(isNeList(activate(V))) U12(tt()) = 8 >= 0 = tt() U21(tt(),V1,V2) = 2V1 + 1V2 + 0 >= 7V1 + 8 = U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) = 8 >= 0 = U23(isList(activate(V2))) U23(tt()) = 0 >= 0 = tt() U31(tt(),V) = V >= V = U32(isQid(activate(V))) U32(tt()) = 0 >= 0 = tt() U41(tt(),V1,V2) = V1 + V2 + 0 >= V2 + 0 = U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) = V2 + 0 >= 0 = U43(isNeList(activate(V2))) U43(tt()) = 0 >= 0 = tt() U51(tt(),V1,V2) = V1 + 5 >= V1 = U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) = 0 >= 0 = U53(isList(activate(V2))) U53(tt()) = 0 >= 0 = tt() U61(tt(),V) = 2V >= 0 = U62(isQid(activate(V))) U62(tt()) = 0 >= 0 = tt() U71(tt(),V) = 2 >= 2 = U72(isNePal(activate(V))) U72(tt()) = 2 >= 0 = tt() and(tt(),X) = X + 0 >= X = activate(X) isList(V) = 2V + 0 >= 1V + 0 = U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) = 2 >= 0 = tt() isList(n____(V1,V2)) = 4V1 + 2V2 + 7 >= 2V1 + 1V2 + 0 = U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(V) = V >= V = U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) = 2V1 + V2 + 5 >= V1 + V2 + 0 = U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(n____(V1,V2)) = 2V1 + V2 + 5 >= V1 + 5 = U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNePal(V) = 0 >= 2V = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 0 >= I + 4 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) isPal(V) = 4 >= 2 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 4 >= 0 = tt() 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)) = 0 >= 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) = 0 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 4 >= 0 = tt() isQid(n__o()) = 5 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = n____(X1,X2) isPalListKind(X) = 0 >= 0 = n__isPalListKind(X) and(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = n__and(X1,X2) isPal(X) = 4 >= 4 = n__isPal(X) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 4 >= 4 = n__i() o() = 5 >= 5 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = 0 >= 0 = isPalListKind(X) activate(n__and(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(activate(X1),X2) activate(n__isPal(X)) = 4 >= 4 = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 4 >= 4 = i() activate(n__o()) = 5 >= 5 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X problem: 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) -> 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Restore Modifier: 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) -> 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 usable rules: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X 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() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) 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)) 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))) nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 interpretation: [U52](x0, x1) = 0, [U22#](x0, x1) = 2x1 + 1, [activate](x0) = x0, [U42](x0, x1) = 1, [isList](x0) = 0, [nil] = 0, [U11](x0, x1) = 0, [U43](x0) = 0, [U62](x0) = 4x0, [n__o] = 0, [isPalListKind](x0) = 4, [isPal](x0) = 4x0 + 1, [U53](x0) = 0, [U51](x0, x1, x2) = 0, [n__nil] = 0, [n__e] = 0, [U71](x0, x1) = 4x1, [n____](x0, x1) = x0 + x1 + 2, [U11#](x0, x1) = 2x1, [isNeList](x0) = 4, [n__a] = 2, [U23](x0) = 4, [__](x0, x1) = x0 + x1 + 2, [e] = 0, [U21](x0, x1, x2) = 6x0 + x1 + 2, [U61](x0, x1) = 4x1 + 2, [and](x0, x1) = x1, [isList#](x0) = 2x0, [n__isPal](x0) = 4x0 + 1, [U41](x0, x1, x2) = 4, [U42#](x0, x1) = 2x1, [n__and](x0, x1) = x1, [isQid](x0) = 2, [isNePal](x0) = 7, [U72](x0) = 0, [U31](x0, x1) = 4, [U22](x0, x1) = 7, [U32](x0) = 4, [i] = 0, [U41#](x0, x1, x2) = 2x1 + 2x2, [U52#](x0, x1) = 2x1, [U12](x0) = 0, [a] = 2, [U51#](x0, x1, x2) = x0 + 2x1 + 2x2, [U21#](x0, x1, x2) = 2x1 + 2x2 + 1, [n__u] = 0, [o] = 0, [u] = 0, [isNeList#](x0) = 2x0, [n__i] = 0, [n__isPalListKind](x0) = 4, [tt] = 0 orientation: U52#(tt(),V2) = 2V2 >= 2V2 = isList#(activate(V2)) isList#(V) = 2V >= 2V = U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) = 2V >= 2V = isNeList#(activate(V)) isNeList#(n____(V1,V2)) = 2V1 + 2V2 + 4 >= 2V1 + 2V2 = U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U41#(tt(),V1,V2) = 2V1 + 2V2 >= 2V1 = isList#(activate(V1)) isList#(n____(V1,V2)) = 2V1 + 2V2 + 4 >= 2V1 + 2V2 + 1 = U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U21#(tt(),V1,V2) = 2V1 + 2V2 + 1 >= 2V1 = isList#(activate(V1)) U21#(tt(),V1,V2) = 2V1 + 2V2 + 1 >= 2V2 + 1 = U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) = 2V2 + 1 >= 2V2 = isList#(activate(V2)) U41#(tt(),V1,V2) = 2V1 + 2V2 >= 2V2 = U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) = 2V2 >= 2V2 = isNeList#(activate(V2)) isNeList#(n____(V1,V2)) = 2V1 + 2V2 + 4 >= 2V1 + 2V2 + 4 = U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U51#(tt(),V1,V2) = 2V1 + 2V2 >= 2V2 = U52#(isNeList(activate(V1)),activate(V2)) __(__(X,Y),Z) = X + Y + Z + 4 >= X + Y + Z + 4 = __(X,__(Y,Z)) __(X,nil()) = X + 2 >= X = X __(nil(),X) = X + 2 >= X = X U11(tt(),V) = 0 >= 0 = U12(isNeList(activate(V))) U12(tt()) = 0 >= 0 = tt() U21(tt(),V1,V2) = V1 + 2 >= 7 = U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) = 7 >= 4 = U23(isList(activate(V2))) U23(tt()) = 4 >= 0 = tt() U31(tt(),V) = 4 >= 4 = U32(isQid(activate(V))) U32(tt()) = 4 >= 0 = tt() U41(tt(),V1,V2) = 4 >= 1 = U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) = 1 >= 0 = U43(isNeList(activate(V2))) U43(tt()) = 0 >= 0 = tt() U51(tt(),V1,V2) = 0 >= 0 = U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) = 0 >= 0 = U53(isList(activate(V2))) U53(tt()) = 0 >= 0 = tt() U61(tt(),V) = 4V + 2 >= 8 = U62(isQid(activate(V))) U62(tt()) = 0 >= 0 = tt() U71(tt(),V) = 4V >= 0 = U72(isNePal(activate(V))) U72(tt()) = 0 >= 0 = tt() and(tt(),X) = X >= X = activate(X) isList(V) = 0 >= 0 = U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) = 0 >= 0 = tt() isList(n____(V1,V2)) = 0 >= V1 + 26 = U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(V) = 4 >= 4 = U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) = 4 >= 4 = U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(n____(V1,V2)) = 4 >= 0 = U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNePal(V) = 7 >= 4V + 2 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 7 >= 4 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) isPal(V) = 4V + 1 >= 4V = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 1 >= 0 = tt() isPalListKind(n__a()) = 4 >= 0 = tt() isPalListKind(n__e()) = 4 >= 0 = tt() isPalListKind(n__i()) = 4 >= 0 = tt() isPalListKind(n__nil()) = 4 >= 0 = tt() isPalListKind(n__o()) = 4 >= 0 = tt() isPalListKind(n__u()) = 4 >= 0 = tt() isPalListKind(n____(V1,V2)) = 4 >= 4 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) = 2 >= 0 = tt() isQid(n__e()) = 2 >= 0 = tt() isQid(n__i()) = 2 >= 0 = tt() isQid(n__o()) = 2 >= 0 = tt() isQid(n__u()) = 2 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = n____(X1,X2) isPalListKind(X) = 4 >= 4 = n__isPalListKind(X) and(X1,X2) = X2 >= X2 = n__and(X1,X2) isPal(X) = 4X + 1 >= 4X + 1 = n__isPal(X) a() = 2 >= 2 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = 4 >= 4 = isPalListKind(X) activate(n__and(X1,X2)) = X2 >= X2 = and(activate(X1),X2) activate(n__isPal(X)) = 4X + 1 >= 4X + 1 = isPal(X) activate(n__a()) = 2 >= 2 = 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 >= X = X problem: DPs: U52#(tt(),V2) -> isList#(activate(V2)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) U41#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),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) -> 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Restore Modifier: DPs: U52#(tt(),V2) -> isList#(activate(V2)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) U41#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),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) -> 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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: 5 #arcs: 24/81 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)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and ( n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 usable rules: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X 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) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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))) nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 interpretation: [U52](x0, x1) = 2x1, [activate](x0) = x0, [U42](x0, x1) = 3x0, [isList](x0) = 4x0 + 7, [nil] = 0, [U11](x0, x1) = 4x1 + 3, [U43](x0) = 2, [U62](x0) = 1, [n__o] = 0, [isPalListKind](x0) = 0, [isPal](x0) = 4, [U53](x0) = x0, [U51](x0, x1, x2) = 7x2 + 3, [n__nil] = 0, [n__e] = 0, [U71](x0, x1) = 4, [n____](x0, x1) = 2x0 + x1 + 1, [U11#](x0, x1) = 4x1 + 2, [isNeList](x0) = 0, [n__a] = 4, [U23](x0) = 0, [__](x0, x1) = 2x0 + x1 + 1, [e] = 0, [U21](x0, x1, x2) = 4x2 + 6, [U61](x0, x1) = 1, [and](x0, x1) = 2x1, [isList#](x0) = 4x0 + 2, [n__isPal](x0) = 4, [U41](x0, x1, x2) = 1, [n__and](x0, x1) = 2x1, [isQid](x0) = 7, [isNePal](x0) = 4, [U72](x0) = x0, [U31](x0, x1) = 0, [U22](x0, x1) = 0, [U32](x0) = 4x0, [i] = 0, [U52#](x0, x1) = 4x1 + 2, [U12](x0) = 2, [a] = 4, [U51#](x0, x1, x2) = 4x2 + 6, [n__u] = 0, [o] = 0, [u] = 0, [isNeList#](x0) = 4x0 + 2, [n__i] = 0, [n__isPalListKind](x0) = 0, [tt] = 0 orientation: U52#(tt(),V2) = 4V2 + 2 >= 4V2 + 2 = isList#(activate(V2)) isList#(V) = 4V + 2 >= 4V + 2 = U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) = 4V + 2 >= 4V + 2 = isNeList#(activate(V)) isNeList#(n____(V1,V2)) = 8V1 + 4V2 + 6 >= 4V2 + 6 = U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U51#(tt(),V1,V2) = 4V2 + 6 >= 4V2 + 2 = U52#(isNeList(activate(V1)),activate(V2)) __(__(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = __(X,__(Y,Z)) __(X,nil()) = 2X + 1 >= X = X __(nil(),X) = X + 1 >= X = X U11(tt(),V) = 4V + 3 >= 2 = U12(isNeList(activate(V))) U12(tt()) = 2 >= 0 = tt() U21(tt(),V1,V2) = 4V2 + 6 >= 0 = U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) = 0 >= 0 = U23(isList(activate(V2))) U23(tt()) = 0 >= 0 = tt() U31(tt(),V) = 0 >= 28 = U32(isQid(activate(V))) U32(tt()) = 0 >= 0 = tt() U41(tt(),V1,V2) = 1 >= 12V1 + 21 = U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) = 0 >= 2 = U43(isNeList(activate(V2))) U43(tt()) = 2 >= 0 = tt() U51(tt(),V1,V2) = 7V2 + 3 >= 2V2 = U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) = 2V2 >= 4V2 + 7 = U53(isList(activate(V2))) U53(tt()) = 0 >= 0 = tt() U61(tt(),V) = 1 >= 1 = U62(isQid(activate(V))) U62(tt()) = 1 >= 0 = tt() U71(tt(),V) = 4 >= 4 = U72(isNePal(activate(V))) U72(tt()) = 0 >= 0 = tt() and(tt(),X) = 2X >= X = activate(X) isList(V) = 4V + 7 >= 4V + 3 = U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) = 7 >= 0 = tt() isList(n____(V1,V2)) = 8V1 + 4V2 + 11 >= 4V2 + 6 = U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(V) = 0 >= 0 = U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) = 0 >= 1 = U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(n____(V1,V2)) = 0 >= 7V2 + 3 = U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNePal(V) = 4 >= 1 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 4 >= 0 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) isPal(V) = 4 >= 4 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 4 >= 0 = tt() 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)) = 0 >= 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) = 7 >= 0 = tt() isQid(n__e()) = 7 >= 0 = tt() isQid(n__i()) = 7 >= 0 = tt() isQid(n__o()) = 7 >= 0 = tt() isQid(n__u()) = 7 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = n____(X1,X2) isPalListKind(X) = 0 >= 0 = n__isPalListKind(X) and(X1,X2) = 2X2 >= 2X2 = n__and(X1,X2) isPal(X) = 4 >= 4 = n__isPal(X) a() = 4 >= 4 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = 0 >= 0 = isPalListKind(X) activate(n__and(X1,X2)) = 2X2 >= 2X2 = and(activate(X1),X2) activate(n__isPal(X)) = 4 >= 4 = isPal(X) activate(n__a()) = 4 >= 4 = 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 >= X = X problem: 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)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Restore Modifier: 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)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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: 5/16 DPs: isPal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n____(X1,X2)) -> activate#(X1) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> activate#(P) isNePal#(n____(I,n____(P,I))) -> activate#(I) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n____(X1,X2)) -> activate#(X1) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> activate#(P) isNePal#(n____(I,n____(P,I))) -> activate#(I) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (activate(P)))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() interpretation: [activate](x0) = x0, [nil] = 0, [U62](x0) = 6x0 + 4, [n__o] = 0, [isPal#](x0) = x0, [isPalListKind](x0) = x0, [U71#](x0, x1) = x0 + x1, [isPal](x0) = x0, [n__nil] = 0, [n__e] = 2, [U71](x0, x1) = x0 + x1, [n____](x0, x1) = 2x0 + x1 + 0, [n__a] = 0, [isNePal#](x0) = x0 + 0, [__](x0, x1) = 2x0 + x1 + 0, [e] = 2, [U61](x0, x1) = x0 + 3, [and](x0, x1) = 1x0 + x1 + 0, [n__isPal](x0) = x0, [n__and](x0, x1) = 1x0 + x1 + 0, [isQid](x0) = 1, [activate#](x0) = x0, [isNePal](x0) = 3x0 + 0, [U72](x0) = 0, [i] = 2, [isPalListKind#](x0) = x0, [a] = 0, [U61#](x0, x1) = x1 + 0, [n__u] = 0, [o] = 0, [u] = 0, [and#](x0, x1) = x1 + 0, [n__i] = 2, [n__isPalListKind](x0) = x0, [tt] = 0 orientation: isPal#(V) = V >= V = isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) = 2V1 + V2 + 0 >= V2 = activate#(V2) activate#(n____(X1,X2)) = 2X1 + X2 + 0 >= X2 = activate#(X2) activate#(n____(X1,X2)) = 2X1 + X2 + 0 >= X1 = activate#(X1) activate#(n__isPalListKind(X)) = X >= X = isPalListKind#(X) isPalListKind#(n____(V1,V2)) = 2V1 + V2 + 0 >= V1 = activate#(V1) activate#(n__and(X1,X2)) = 1X1 + X2 + 0 >= X1 = activate#(X1) activate#(n__and(X1,X2)) = 1X1 + X2 + 0 >= X2 + 0 = and#(activate(X1),X2) and#(tt(),X) = X + 0 >= X = activate#(X) activate#(n__isPal(X)) = X >= X = isPal#(X) isPal#(V) = V >= V = activate#(V) isPal#(V) = V >= V = U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) = V + 0 >= V = activate#(V) U71#(tt(),V) = V + 0 >= V + 0 = isNePal#(activate(V)) isNePal#(V) = V + 0 >= V = activate#(V) isNePal#(V) = V + 0 >= V = isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) = 2V1 + V2 + 0 >= V1 = isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) = 2V1 + V2 + 0 >= V2 + 0 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) = V + 0 >= V + 0 = U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) = V + 0 >= V = activate#(V) isNePal#(n____(I,n____(P,I))) = 2I + 2P + 0 >= P = activate#(P) isNePal#(n____(I,n____(P,I))) = 2I + 2P + 0 >= I = activate#(I) isNePal#(n____(I,n____(P,I))) = 2I + 2P + 0 >= I + 0 = and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) = 2I + 2P + 0 >= 1P + 0 = and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate (P)), n__isPalListKind (activate (P)))) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 2X1 + X2 + 0 >= 2X1 + X2 + 0 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = X >= X = isPalListKind(X) activate(n__and(X1,X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = and(activate(X1),X2) activate(n__isPal(X)) = X >= X = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 2 >= 2 = e() activate(n__i()) = 2 >= 2 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X nil() = 0 >= 0 = n__nil() __(__(X,Y),Z) = 4X + 2Y + Z + 2 >= 2X + 2Y + Z + 0 = __(X,__(Y,Z)) __(X,nil()) = 2X + 0 >= X = X __(nil(),X) = X + 2 >= X = X __(X1,X2) = 2X1 + X2 + 0 >= 2X1 + X2 + 0 = n____(X1,X2) isPalListKind(n__a()) = 0 >= 0 = tt() isPalListKind(n__e()) = 2 >= 0 = tt() isPalListKind(n__i()) = 2 >= 0 = tt() isPalListKind(n__nil()) = 0 >= 0 = tt() isPalListKind(n__o()) = 0 >= 0 = tt() isPalListKind(n__u()) = 0 >= 0 = tt() isPalListKind(n____(V1,V2)) = 2V1 + V2 + 0 >= 1V1 + V2 + 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = X >= X = n__isPalListKind(X) and(tt(),X) = X + 1 >= X = activate(X) and(X1,X2) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = n__and(X1,X2) isPal(V) = V >= V = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 0 >= 0 = tt() isPal(X) = X >= X = n__isPal(X) U71(tt(),V) = V + 0 >= 0 = U72(isNePal(activate(V))) U72(tt()) = 0 >= 0 = tt() isNePal(V) = 3V + 0 >= V + 3 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 5I + 5P + 3 >= 1I + 1P + 3 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = 3 >= 7 = U62(isQid(activate(V))) U62(tt()) = 6 >= 0 = tt() isQid(n__a()) = 1 >= 0 = tt() isQid(n__e()) = 1 >= 0 = tt() isQid(n__i()) = 1 >= 0 = tt() isQid(n__o()) = 1 >= 0 = tt() isQid(n__u()) = 1 >= 0 = tt() a() = 0 >= 0 = n__a() e() = 2 >= 2 = n__e() i() = 2 >= 2 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() problem: DPs: isPal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (activate(P)))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Restore Modifier: DPs: isPal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> activate#(V) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and ( n__isPal(activate(P)), n__isPalListKind (activate(P)))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__isPal(activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() interpretation: [activate](x0) = x0 + 0, [nil] = 0, [U62](x0) = 3x0 + 0, [n__o] = 0, [isPal#](x0) = 7x0 + 7, [isPalListKind](x0) = x0 + 0, [U71#](x0, x1) = 7x1 + 7, [isPal](x0) = 7x0 + 7, [n__nil] = 0, [n__e] = 0, [U71](x0, x1) = 7x1 + 0, [n____](x0, x1) = x0 + x1, [n__a] = 0, [isNePal#](x0) = 7x0 + 0, [__](x0, x1) = x0 + x1 + 0, [e] = 0, [U61](x0, x1) = x1, [and](x0, x1) = x1 + 0, [n__isPal](x0) = 7x0 + 7, [n__and](x0, x1) = x1 + 0, [isQid](x0) = x0 + 0, [activate#](x0) = x0, [isNePal](x0) = 0, [U72](x0) = 0, [i] = 0, [isPalListKind#](x0) = x0 + 0, [a] = 0, [U61#](x0, x1) = x0 + x1 + 0, [n__u] = 0, [o] = 0, [u] = 0, [and#](x0, x1) = x1 + 0, [n__i] = 0, [n__isPalListKind](x0) = x0 + 0, [tt] = 0 orientation: isPal#(V) = 7V + 7 >= V + 0 = isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) = V1 + V2 + 0 >= V2 = activate#(V2) activate#(n____(X1,X2)) = X1 + X2 >= X2 = activate#(X2) activate#(n__isPalListKind(X)) = X + 0 >= X + 0 = isPalListKind#(X) activate#(n__and(X1,X2)) = X2 + 0 >= X2 + 0 = and#(activate(X1),X2) and#(tt(),X) = X + 0 >= X = activate#(X) activate#(n__isPal(X)) = 7X + 7 >= 7X + 7 = isPal#(X) isPal#(V) = 7V + 7 >= V = activate#(V) isPal#(V) = 7V + 7 >= 7V + 7 = U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) = 7V + 7 >= V = activate#(V) U71#(tt(),V) = 7V + 7 >= 7V + 7 = isNePal#(activate(V)) isNePal#(V) = 7V + 0 >= V = activate#(V) isNePal#(V) = 7V + 0 >= V + 0 = isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) = V1 + V2 + 0 >= V2 + 0 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) = 7V + 0 >= V + 0 = U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) = V + 0 >= V = activate#(V) isNePal#(n____(I,n____(P,I))) = 7I + 7P + 0 >= I + 0 = and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) = 7I + 7P + 0 >= P + 0 = and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate (P)), n__isPalListKind (activate (P)))) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = X + 0 >= X + 0 = isPalListKind(X) activate(n__and(X1,X2)) = X2 + 0 >= X2 + 0 = and(activate(X1),X2) activate(n__isPal(X)) = 7X + 7 >= 7X + 7 = isPal(X) 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) = X + Y + Z + 0 >= X + Y + Z + 0 = __(X,__(Y,Z)) __(X,nil()) = X + 0 >= X = X __(nil(),X) = X + 0 >= X = X __(X1,X2) = X1 + X2 + 0 >= X1 + X2 = 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)) = V1 + V2 + 0 >= V2 + 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = X + 0 >= X + 0 = n__isPalListKind(X) and(tt(),X) = X + 0 >= X + 0 = activate(X) and(X1,X2) = X2 + 0 >= X2 + 0 = n__and(X1,X2) isPal(V) = 7V + 7 >= 7V + 7 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 7 >= 0 = tt() isPal(X) = 7X + 7 >= 7X + 7 = n__isPal(X) U71(tt(),V) = 7V + 0 >= 0 = U72(isNePal(activate(V))) U72(tt()) = 0 >= 0 = tt() isNePal(V) = 0 >= V + 0 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 0 >= P + 0 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = V >= 3V + 3 = U62(isQid(activate(V))) U62(tt()) = 3 >= 0 = tt() isQid(n__a()) = 0 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 0 >= 0 = tt() isQid(n__o()) = 0 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() 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: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Restore Modifier: DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(V) -> isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Arctic Interpretation Processor: dimension: 1 usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() interpretation: [activate](x0) = x0 + 0, [nil] = 0, [U62](x0) = 1x0 + 0, [n__o] = 1, [isPal#](x0) = 4x0 + 4, [isPalListKind](x0) = x0 + 0, [U71#](x0, x1) = 4x0 + 4x1 + 0, [isPal](x0) = 4x0 + 4, [n__nil] = 0, [n__e] = 0, [U71](x0, x1) = 2x0 + 1x1 + 0, [n____](x0, x1) = x0 + x1, [n__a] = 0, [isNePal#](x0) = 4x0 + 4, [__](x0, x1) = x0 + x1 + 0, [e] = 0, [U61](x0, x1) = 2x1 + 0, [and](x0, x1) = x0 + x1 + 0, [n__isPal](x0) = 4x0 + 4, [n__and](x0, x1) = x0 + x1 + 0, [isQid](x0) = 2x0 + 4, [activate#](x0) = x0 + 0, [isNePal](x0) = x0 + 0, [U72](x0) = 0, [i] = 0, [isPalListKind#](x0) = x0 + 0, [a] = 0, [U61#](x0, x1) = x0 + x1 + 0, [n__u] = 0, [o] = 1, [u] = 0, [and#](x0, x1) = x0 + x1 + 0, [n__i] = 0, [n__isPalListKind](x0) = x0 + 0, [tt] = 0 orientation: isPalListKind#(n____(V1,V2)) = V1 + V2 + 0 >= V2 + 0 = activate#(V2) activate#(n____(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = activate#(X2) activate#(n__isPalListKind(X)) = X + 0 >= X + 0 = isPalListKind#(X) activate#(n__and(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and#(activate(X1),X2) and#(tt(),X) = X + 0 >= X + 0 = activate#(X) activate#(n__isPal(X)) = 4X + 4 >= 4X + 4 = isPal#(X) isPal#(V) = 4V + 4 >= 4V + 4 = U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) = 4V + 4 >= 4V + 4 = isNePal#(activate(V)) isNePal#(V) = 4V + 4 >= V + 0 = isPalListKind#(activate(V)) isPalListKind#(n____(V1,V2)) = V1 + V2 + 0 >= V1 + V2 + 0 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) = 4V + 4 >= V + 0 = U61#(isPalListKind(activate(V)),activate(V)) U61#(tt(),V) = V + 0 >= V + 0 = activate#(V) isNePal#(n____(I,n____(P,I))) = 4I + 4P + 4 >= 2I + 4 = and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) = 4I + 4P + 4 >= 2I + 4P + 4 = and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate (P)), n__isPalListKind (activate (P)))) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = X + 0 >= X + 0 = isPalListKind(X) activate(n__and(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(activate(X1),X2) activate(n__isPal(X)) = 4X + 4 >= 4X + 4 = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 1 >= 1 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X + 0 >= X = X nil() = 0 >= 0 = n__nil() __(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = __(X,__(Y,Z)) __(X,nil()) = X + 0 >= X = X __(nil(),X) = X + 0 >= X = X __(X1,X2) = X1 + X2 + 0 >= X1 + X2 = 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()) = 1 >= 0 = tt() isPalListKind(n__u()) = 0 >= 0 = tt() isPalListKind(n____(V1,V2)) = V1 + V2 + 0 >= V1 + V2 + 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = X + 0 >= X + 0 = n__isPalListKind(X) and(tt(),X) = X + 0 >= X + 0 = activate(X) and(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = n__and(X1,X2) isPal(V) = 4V + 4 >= 2V + 2 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 4 >= 0 = tt() isPal(X) = 4X + 4 >= 4X + 4 = n__isPal(X) U71(tt(),V) = 1V + 2 >= 0 = U72(isNePal(activate(V))) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 1 >= 1 = n__o() u() = 0 >= 0 = n__u() U72(tt()) = 0 >= 0 = tt() isNePal(V) = V + 0 >= 2V + 2 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = I + P + 0 >= 2I + 4P + 4 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = 2V + 0 >= 3V + 5 = U62(isQid(activate(V))) U62(tt()) = 1 >= 0 = tt() isQid(n__a()) = 4 >= 0 = tt() isQid(n__e()) = 4 >= 0 = tt() isQid(n__i()) = 4 >= 0 = tt() isQid(n__o()) = 4 >= 0 = tt() isQid(n__u()) = 4 >= 0 = tt() problem: DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Restore Modifier: DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) activate#(n__isPal(X)) -> isPal#(X) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U61#(tt(),V) -> activate#(V) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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: 105/144 DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__isPal(X)) -> isPal#(X) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__isPal(X)) -> isPal#(X) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(n____(I,n____(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() interpretation: [activate](x0) = x0 + 0, [nil] = 0, [U62](x0) = x0 + 0, [n__o] = 2, [isPal#](x0) = 5x0 + 5, [isPalListKind](x0) = x0 + 0, [U71#](x0, x1) = 5x1 + 0, [isPal](x0) = 5x0 + 5, [n__nil] = 0, [n__e] = 0, [U71](x0, x1) = 4x0 + 5x1 + 0, [n____](x0, x1) = 1x0 + x1 + 3, [n__a] = 0, [isNePal#](x0) = x0 + 0, [__](x0, x1) = 1x0 + x1 + 3, [e] = 0, [U61](x0, x1) = x0 + x1 + 0, [and](x0, x1) = x1 + 0, [n__isPal](x0) = 5x0 + 5, [n__and](x0, x1) = x1, [isQid](x0) = 0, [activate#](x0) = x0, [isNePal](x0) = 4x0 + 0, [U72](x0) = x0 + 0, [i] = 1, [isPalListKind#](x0) = x0 + 0, [a] = 0, [n__u] = 0, [o] = 2, [u] = 0, [and#](x0, x1) = x1, [n__i] = 1, [n__isPalListKind](x0) = x0 + 0, [tt] = 0 orientation: isPal#(V) = 5V + 5 >= 5V + 5 = U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) = 5V + 0 >= V + 0 = isNePal#(activate(V)) isNePal#(n____(I,n____(P,I))) = 1I + 1P + 3 >= I + 0 = and#(isQid(activate(I)),n__isPalListKind(activate(I))) and#(tt(),X) = X >= X = activate#(X) activate#(n____(X1,X2)) = 1X1 + X2 + 3 >= X2 = activate#(X2) activate#(n__isPalListKind(X)) = X + 0 >= X + 0 = isPalListKind#(X) isPalListKind#(n____(V1,V2)) = 1V1 + V2 + 3 >= V2 = activate#(V2) activate#(n__and(X1,X2)) = X2 >= X2 = and#(activate(X1),X2) activate#(n__isPal(X)) = 5X + 5 >= 5X + 5 = isPal#(X) isPalListKind#(n____(V1,V2)) = 1V1 + V2 + 3 >= V2 + 0 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(n____(I,n____(P,I))) = 1I + 1P + 3 >= P + 0 = and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate (P)), n__isPalListKind (activate (P)))) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 1X1 + X2 + 3 >= 1X1 + X2 + 3 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = X + 0 >= X + 0 = isPalListKind(X) activate(n__and(X1,X2)) = X2 + 0 >= X2 + 0 = and(activate(X1),X2) activate(n__isPal(X)) = 5X + 5 >= 5X + 5 = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 1 >= 1 = i() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X + 0 >= X = X nil() = 0 >= 0 = n__nil() __(__(X,Y),Z) = 2X + 1Y + Z + 4 >= 1X + 1Y + Z + 3 = __(X,__(Y,Z)) __(X,nil()) = 1X + 3 >= X = X __(nil(),X) = X + 3 >= X = X __(X1,X2) = 1X1 + X2 + 3 >= 1X1 + X2 + 3 = n____(X1,X2) isPalListKind(n__a()) = 0 >= 0 = tt() isPalListKind(n__e()) = 0 >= 0 = tt() isPalListKind(n__i()) = 1 >= 0 = tt() isPalListKind(n__nil()) = 0 >= 0 = tt() isPalListKind(n__o()) = 2 >= 0 = tt() isPalListKind(n__u()) = 0 >= 0 = tt() isPalListKind(n____(V1,V2)) = 1V1 + V2 + 3 >= V2 + 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = X + 0 >= X + 0 = n__isPalListKind(X) and(tt(),X) = X + 0 >= X + 0 = activate(X) and(X1,X2) = X2 + 0 >= X2 = n__and(X1,X2) isPal(V) = 5V + 5 >= 5V + 5 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 5 >= 0 = tt() isPal(X) = 5X + 5 >= 5X + 5 = n__isPal(X) U71(tt(),V) = 5V + 4 >= 4V + 4 = U72(isNePal(activate(V))) U72(tt()) = 0 >= 0 = tt() isNePal(V) = 4V + 0 >= V + 0 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 5I + 5P + 7 >= P + 0 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = V + 0 >= 0 = U62(isQid(activate(V))) U62(tt()) = 0 >= 0 = tt() isQid(n__a()) = 0 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 0 >= 0 = tt() isQid(n__o()) = 0 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 1 >= 1 = n__i() o() = 2 >= 2 = n__o() u() = 0 >= 0 = n__u() problem: DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__isPal(X)) -> isPal#(X) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Restore Modifier: DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__isPal(X)) -> isPal#(X) 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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: 6 #arcs: 22/81 DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Arctic Interpretation Processor: dimension: 1 usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() interpretation: [activate](x0) = x0, [nil] = 0, [U62](x0) = x0 + 0, [n__o] = 0, [isPalListKind](x0) = 4x0 + 4, [isPal](x0) = x0 + 0, [n__nil] = 0, [n__e] = 2, [U71](x0, x1) = 0, [n____](x0, x1) = x0 + x1, [n__a] = 0, [__](x0, x1) = x0 + x1, [e] = 2, [U61](x0, x1) = 4x1 + 0, [and](x0, x1) = x0 + x1 + 4, [n__isPal](x0) = x0 + 0, [n__and](x0, x1) = x0 + x1 + 4, [isQid](x0) = 5, [activate#](x0) = x0, [isNePal](x0) = 0, [U72](x0) = 0, [i] = 0, [isPalListKind#](x0) = 4x0 + 4, [a] = 0, [n__u] = 0, [o] = 0, [u] = 0, [and#](x0, x1) = x0 + x1, [n__i] = 0, [n__isPalListKind](x0) = 4x0 + 4, [tt] = 0 orientation: isPalListKind#(n____(V1,V2)) = 4V1 + 4V2 + 4 >= 4V1 + 4V2 + 4 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) = X + 0 >= X = activate#(X) activate#(n____(X1,X2)) = X1 + X2 >= X2 = activate#(X2) activate#(n__isPalListKind(X)) = 4X + 4 >= 4X + 4 = isPalListKind#(X) isPalListKind#(n____(V1,V2)) = 4V1 + 4V2 + 4 >= V2 = activate#(V2) activate#(n__and(X1,X2)) = X1 + X2 + 4 >= X1 + X2 = and#(activate(X1),X2) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = X1 + X2 >= X1 + X2 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = 4X + 4 >= 4X + 4 = isPalListKind(X) activate(n__and(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = and(activate(X1),X2) activate(n__isPal(X)) = X + 0 >= X + 0 = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 2 >= 2 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X nil() = 0 >= 0 = n__nil() __(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z)) __(X,nil()) = X + 0 >= X = X __(nil(),X) = X + 0 >= X = X __(X1,X2) = X1 + X2 >= X1 + X2 = n____(X1,X2) isPalListKind(n__a()) = 4 >= 0 = tt() isPalListKind(n__e()) = 6 >= 0 = tt() isPalListKind(n__i()) = 4 >= 0 = tt() isPalListKind(n__nil()) = 4 >= 0 = tt() isPalListKind(n__o()) = 4 >= 0 = tt() isPalListKind(n__u()) = 4 >= 0 = tt() isPalListKind(n____(V1,V2)) = 4V1 + 4V2 + 4 >= 4V1 + 4V2 + 4 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = 4X + 4 >= 4X + 4 = n__isPalListKind(X) and(tt(),X) = X + 4 >= X = activate(X) and(X1,X2) = X1 + X2 + 4 >= X1 + X2 + 4 = n__and(X1,X2) isPal(V) = V + 0 >= 0 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 0 >= 0 = tt() isPal(X) = X + 0 >= X + 0 = n__isPal(X) U71(tt(),V) = 0 >= 0 = U72(isNePal(activate(V))) a() = 0 >= 0 = n__a() e() = 2 >= 2 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() U72(tt()) = 0 >= 0 = tt() isNePal(V) = 0 >= 4V + 0 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 0 >= 4I + 4P + 5 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = 4V + 0 >= 5 = U62(isQid(activate(V))) U62(tt()) = 0 >= 0 = tt() isQid(n__a()) = 5 >= 0 = tt() isQid(n__e()) = 5 >= 0 = tt() isQid(n__i()) = 5 >= 0 = tt() isQid(n__o()) = 5 >= 0 = tt() isQid(n__u()) = 5 >= 0 = tt() problem: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Restore Modifier: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Arctic Interpretation Processor: dimension: 1 usable rules: interpretation: [activate](x0) = x0, [nil] = 4, [U62](x0) = x0 + 0, [n__o] = 4, [isPalListKind](x0) = x0, [isPal](x0) = x0 + 0, [n__nil] = 3, [n__e] = 0, [U71](x0, x1) = x1 + 3, [n____](x0, x1) = x0 + x1, [n__a] = 1, [__](x0, x1) = 1x0 + 0, [e] = 0, [U61](x0, x1) = x1 + 0, [and](x0, x1) = x0 + x1 + 0, [n__isPal](x0) = 2x0 + 0, [n__and](x0, x1) = 2x0 + 1x1 + 0, [isQid](x0) = 4, [activate#](x0) = x0, [isNePal](x0) = x0 + 2, [U72](x0) = x0 + 0, [i] = 0, [isPalListKind#](x0) = 0, [a] = 0, [n__u] = 2, [o] = 0, [u] = 0, [and#](x0, x1) = x1, [n__i] = 0, [n__isPalListKind](x0) = 0, [tt] = 6 orientation: isPalListKind#(n____(V1,V2)) = 0 >= 0 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) = X >= X = activate#(X) activate#(n____(X1,X2)) = X1 + X2 >= X2 = activate#(X2) activate#(n__isPalListKind(X)) = 0 >= 0 = isPalListKind#(X) activate#(n__and(X1,X2)) = 2X1 + 1X2 + 0 >= X2 = and#(activate(X1),X2) activate(n__nil()) = 3 >= 4 = nil() activate(n____(X1,X2)) = X1 + X2 >= 1X1 + 0 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = 0 >= X = isPalListKind(X) activate(n__and(X1,X2)) = 2X1 + 1X2 + 0 >= X1 + X2 + 0 = and(activate(X1),X2) activate(n__isPal(X)) = 2X + 0 >= X + 0 = isPal(X) activate(n__a()) = 1 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 4 >= 0 = o() activate(n__u()) = 2 >= 0 = u() activate(X) = X >= X = X nil() = 4 >= 3 = n__nil() __(__(X,Y),Z) = 2X + 1 >= 1X + 0 = __(X,__(Y,Z)) __(X,nil()) = 1X + 0 >= X = X __(nil(),X) = 5 >= X = X __(X1,X2) = 1X1 + 0 >= X1 + X2 = n____(X1,X2) isPalListKind(n__a()) = 1 >= 6 = tt() isPalListKind(n__e()) = 0 >= 6 = tt() isPalListKind(n__i()) = 0 >= 6 = tt() isPalListKind(n__nil()) = 3 >= 6 = tt() isPalListKind(n__o()) = 4 >= 6 = tt() isPalListKind(n__u()) = 2 >= 6 = tt() isPalListKind(n____(V1,V2)) = V1 + V2 >= V1 + 0 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = X >= 0 = n__isPalListKind(X) and(tt(),X) = X + 6 >= X = activate(X) and(X1,X2) = X1 + X2 + 0 >= 2X1 + 1X2 + 0 = n__and(X1,X2) isPal(V) = V + 0 >= V + 3 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 3 >= 6 = tt() isPal(X) = X + 0 >= 2X + 0 = n__isPal(X) U71(tt(),V) = V + 3 >= V + 2 = U72(isNePal(activate(V))) a() = 0 >= 1 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 4 = n__o() u() = 0 >= 2 = n__u() U72(tt()) = 6 >= 6 = tt() isNePal(V) = V + 2 >= V + 0 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = I + P + 2 >= 4P + 4 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = V + 0 >= 4 = U62(isQid(activate(V))) U62(tt()) = 6 >= 6 = tt() isQid(n__a()) = 4 >= 6 = tt() isQid(n__e()) = 4 >= 6 = tt() isQid(n__i()) = 4 >= 6 = tt() isQid(n__o()) = 4 >= 6 = tt() isQid(n__u()) = 4 >= 6 = tt() problem: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Restore Modifier: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n____(X1,X2)) -> activate#(X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Arctic Interpretation Processor: dimension: 1 usable rules: interpretation: [activate](x0) = x0 + 2, [nil] = 0, [U62](x0) = 1x0 + 0, [n__o] = 3, [isPalListKind](x0) = 2x0 + 0, [isPal](x0) = 5, [n__nil] = 5, [n__e] = 2, [U71](x0, x1) = 3x0 + 5x1 + 8, [n____](x0, x1) = 4x0 + 2x1 + 5, [n__a] = 0, [__](x0, x1) = 1x0 + 1, [e] = 0, [U61](x0, x1) = 2x0 + 5x1 + 4, [and](x0, x1) = 2x1, [n__isPal](x0) = 0, [n__and](x0, x1) = x0 + 2x1 + 0, [isQid](x0) = 1x0 + 5, [activate#](x0) = x0 + 0, [isNePal](x0) = x0 + 1, [U72](x0) = 2x0 + 0, [i] = 2, [isPalListKind#](x0) = 0, [a] = 0, [n__u] = 2, [o] = 2, [u] = 0, [and#](x0, x1) = x1 + 0, [n__i] = 4, [n__isPalListKind](x0) = 0, [tt] = 0 orientation: isPalListKind#(n____(V1,V2)) = 0 >= 0 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) = X + 0 >= X + 0 = activate#(X) activate#(n____(X1,X2)) = 4X1 + 2X2 + 5 >= X2 + 0 = activate#(X2) activate#(n__isPalListKind(X)) = 0 >= 0 = isPalListKind#(X) activate(n__nil()) = 5 >= 0 = nil() activate(n____(X1,X2)) = 4X1 + 2X2 + 5 >= 1X1 + 3 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = 2 >= 2X + 0 = isPalListKind(X) activate(n__and(X1,X2)) = X1 + 2X2 + 2 >= 2X2 = and(activate(X1),X2) activate(n__isPal(X)) = 2 >= 5 = isPal(X) activate(n__a()) = 2 >= 0 = a() activate(n__e()) = 2 >= 0 = e() activate(n__i()) = 4 >= 2 = i() activate(n__o()) = 3 >= 2 = o() activate(n__u()) = 2 >= 0 = u() activate(X) = X + 2 >= X = X nil() = 0 >= 5 = n__nil() __(__(X,Y),Z) = 2X + 2 >= 1X + 1 = __(X,__(Y,Z)) __(X,nil()) = 1X + 1 >= X = X __(nil(),X) = 1 >= X = X __(X1,X2) = 1X1 + 1 >= 4X1 + 2X2 + 5 = n____(X1,X2) isPalListKind(n__a()) = 2 >= 0 = tt() isPalListKind(n__e()) = 4 >= 0 = tt() isPalListKind(n__i()) = 6 >= 0 = tt() isPalListKind(n__nil()) = 7 >= 0 = tt() isPalListKind(n__o()) = 5 >= 0 = tt() isPalListKind(n__u()) = 4 >= 0 = tt() isPalListKind(n____(V1,V2)) = 6V1 + 4V2 + 7 >= 2 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = 2X + 0 >= 0 = n__isPalListKind(X) and(tt(),X) = 2X >= X + 2 = activate(X) and(X1,X2) = 2X2 >= X1 + 2X2 + 0 = n__and(X1,X2) isPal(V) = 5 >= 5V + 8 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 5 >= 0 = tt() isPal(X) = 5 >= 0 = n__isPal(X) U71(tt(),V) = 5V + 8 >= 2V + 4 = U72(isNePal(activate(V))) a() = 0 >= 0 = n__a() e() = 0 >= 2 = n__e() i() = 2 >= 4 = n__i() o() = 2 >= 3 = n__o() u() = 0 >= 2 = n__u() U72(tt()) = 2 >= 0 = tt() isNePal(V) = V + 1 >= 5V + 7 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 4I + 6P + 7 >= 4 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = 5V + 4 >= 2V + 6 = U62(isQid(activate(V))) U62(tt()) = 1 >= 0 = tt() isQid(n__a()) = 5 >= 0 = tt() isQid(n__e()) = 5 >= 0 = tt() isQid(n__i()) = 5 >= 0 = tt() isQid(n__o()) = 5 >= 0 = tt() isQid(n__u()) = 5 >= 0 = tt() problem: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n__isPalListKind(X)) -> isPalListKind#(X) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Restore Modifier: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n__isPalListKind(X)) -> isPalListKind#(X) 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 Usable Rule Processor: DPs: isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n__isPalListKind(X)) -> isPalListKind#(X) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Matrix Interpretation Processor: dim=1 usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() interpretation: [activate](x0) = x0, [nil] = 2, [U62](x0) = 0, [n__o] = 2, [isPalListKind](x0) = 4x0 + 1, [isPal](x0) = x0 + 4, [n__nil] = 2, [n__e] = 1, [U71](x0, x1) = x1 + 4, [n____](x0, x1) = x0 + x1 + 4, [n__a] = 1, [__](x0, x1) = x0 + x1 + 4, [e] = 1, [U61](x0, x1) = x0 + 4, [and](x0, x1) = x1 + 4, [n__isPal](x0) = x0 + 4, [n__and](x0, x1) = x1 + 4, [isQid](x0) = 0, [activate#](x0) = x0 + 6, [isNePal](x0) = 1, [U72](x0) = 4, [i] = 1, [isPalListKind#](x0) = 4x0 + 7, [a] = 1, [n__u] = 5, [o] = 2, [u] = 5, [and#](x0, x1) = x0 + x1 + 2, [n__i] = 1, [n__isPalListKind](x0) = 4x0 + 1, [tt] = 4 orientation: isPalListKind#(n____(V1,V2)) = 4V1 + 4V2 + 23 >= 4V1 + 4V2 + 4 = and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) and#(tt(),X) = X + 6 >= X + 6 = activate#(X) activate#(n__isPalListKind(X)) = 4X + 7 >= 4X + 7 = isPalListKind#(X) activate(n__nil()) = 2 >= 2 = nil() activate(n____(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) = 4X + 1 >= 4X + 1 = isPalListKind(X) activate(n__and(X1,X2)) = X2 + 4 >= X2 + 4 = and(activate(X1),X2) activate(n__isPal(X)) = X + 4 >= X + 4 = isPal(X) activate(n__a()) = 1 >= 1 = a() activate(n__e()) = 1 >= 1 = e() activate(n__i()) = 1 >= 1 = i() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 5 >= 5 = u() activate(X) = X >= X = X nil() = 2 >= 2 = n__nil() __(__(X,Y),Z) = X + Y + Z + 8 >= X + Y + Z + 8 = __(X,__(Y,Z)) __(X,nil()) = X + 6 >= X = X __(nil(),X) = X + 6 >= X = X __(X1,X2) = X1 + X2 + 4 >= X1 + X2 + 4 = n____(X1,X2) isPalListKind(n__a()) = 5 >= 4 = tt() isPalListKind(n__e()) = 5 >= 4 = tt() isPalListKind(n__i()) = 5 >= 4 = tt() isPalListKind(n__nil()) = 9 >= 4 = tt() isPalListKind(n__o()) = 9 >= 4 = tt() isPalListKind(n__u()) = 21 >= 4 = tt() isPalListKind(n____(V1,V2)) = 4V1 + 4V2 + 17 >= 4V2 + 5 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = 4X + 1 >= 4X + 1 = n__isPalListKind(X) and(tt(),X) = X + 4 >= X = activate(X) and(X1,X2) = X2 + 4 >= X2 + 4 = n__and(X1,X2) isPal(V) = V + 4 >= V + 4 = U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) = 6 >= 4 = tt() isPal(X) = X + 4 >= X + 4 = n__isPal(X) U71(tt(),V) = V + 4 >= 4 = U72(isNePal(activate(V))) a() = 1 >= 1 = n__a() e() = 1 >= 1 = n__e() i() = 1 >= 1 = n__i() o() = 2 >= 2 = n__o() u() = 5 >= 5 = n__u() U72(tt()) = 4 >= 4 = tt() isNePal(V) = 1 >= 4V + 5 = U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) = 1 >= 4P + 9 = and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(n__isPal (activate(P)), n__isPalListKind (activate(P)))) U61(tt(),V) = 8 >= 0 = U62(isQid(activate(V))) U62(tt()) = 0 >= 4 = tt() isQid(n__a()) = 0 >= 4 = tt() isQid(n__e()) = 0 >= 4 = tt() isQid(n__i()) = 0 >= 4 = tt() isQid(n__o()) = 0 >= 4 = tt() isQid(n__u()) = 0 >= 4 = tt() problem: DPs: and#(tt(),X) -> activate#(X) activate#(n__isPalListKind(X)) -> isPalListKind#(X) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPal(X) -> n__isPal(X) U71(tt(),V) -> U72(isNePal(activate(V))) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() U72(tt()) -> tt() isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)),n__isPalListKind(activate(P)))) U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() Restore Modifier: DPs: and#(tt(),X) -> activate#(X) activate#(n__isPalListKind(X)) -> isPalListKind#(X) 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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: 13/4 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and( n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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 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,n____(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (n__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) 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)) -> __(activate(X1),activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) 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