/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Proof: DP Processor: DPs: __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) U11#(tt(),V) -> activate#(V) U11#(tt(),V) -> isNeList#(activate(V)) U11#(tt(),V) -> U12#(isNeList(activate(V))) U21#(tt(),V1,V2) -> activate#(V2) U21#(tt(),V1,V2) -> activate#(V1) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> activate#(V2) U22#(tt(),V2) -> isList#(activate(V2)) U22#(tt(),V2) -> U23#(isList(activate(V2))) U31#(tt(),V) -> activate#(V) U31#(tt(),V) -> isQid#(activate(V)) U31#(tt(),V) -> U32#(isQid(activate(V))) U41#(tt(),V1,V2) -> activate#(V2) U41#(tt(),V1,V2) -> activate#(V1) U41#(tt(),V1,V2) -> isList#(activate(V1)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> activate#(V2) U42#(tt(),V2) -> isNeList#(activate(V2)) U42#(tt(),V2) -> U43#(isNeList(activate(V2))) U51#(tt(),V1,V2) -> activate#(V2) U51#(tt(),V1,V2) -> activate#(V1) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) U52#(tt(),V2) -> activate#(V2) U52#(tt(),V2) -> isList#(activate(V2)) U52#(tt(),V2) -> U53#(isList(activate(V2))) U61#(tt(),V) -> activate#(V) U61#(tt(),V) -> isQid#(activate(V)) U61#(tt(),V) -> U62#(isQid(activate(V))) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) U71#(tt(),V) -> U72#(isNePal(activate(V))) and#(tt(),X) -> activate#(X) isList#(V) -> activate#(V) isList#(V) -> isPalListKind#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(V) -> activate#(V) isNeList#(V) -> isPalListKind#(activate(V)) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) isNePal#(n____(I,__(P,I))) -> activate#(I) isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and( isPal(activate(P)), n__isPalListKind (activate(P)))) isPal#(V) -> activate#(V) isPal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) isPalListKind#(n____(V1,V2)) -> activate#(V1) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(X1,X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(X1,X2) activate#(n__a()) -> a#() activate#(n__e()) -> e#() activate#(n__i()) -> i#() activate#(n__o()) -> o#() activate#(n__u()) -> u#() TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X TDG Processor: DPs: __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) U11#(tt(),V) -> activate#(V) U11#(tt(),V) -> isNeList#(activate(V)) U11#(tt(),V) -> U12#(isNeList(activate(V))) U21#(tt(),V1,V2) -> activate#(V2) U21#(tt(),V1,V2) -> activate#(V1) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> activate#(V2) U22#(tt(),V2) -> isList#(activate(V2)) U22#(tt(),V2) -> U23#(isList(activate(V2))) U31#(tt(),V) -> activate#(V) U31#(tt(),V) -> isQid#(activate(V)) U31#(tt(),V) -> U32#(isQid(activate(V))) U41#(tt(),V1,V2) -> activate#(V2) U41#(tt(),V1,V2) -> activate#(V1) U41#(tt(),V1,V2) -> isList#(activate(V1)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> activate#(V2) U42#(tt(),V2) -> isNeList#(activate(V2)) U42#(tt(),V2) -> U43#(isNeList(activate(V2))) U51#(tt(),V1,V2) -> activate#(V2) U51#(tt(),V1,V2) -> activate#(V1) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) U52#(tt(),V2) -> activate#(V2) U52#(tt(),V2) -> isList#(activate(V2)) U52#(tt(),V2) -> U53#(isList(activate(V2))) U61#(tt(),V) -> activate#(V) U61#(tt(),V) -> isQid#(activate(V)) U61#(tt(),V) -> U62#(isQid(activate(V))) U71#(tt(),V) -> activate#(V) U71#(tt(),V) -> isNePal#(activate(V)) U71#(tt(),V) -> U72#(isNePal(activate(V))) and#(tt(),X) -> activate#(X) isList#(V) -> activate#(V) isList#(V) -> isPalListKind#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(V) -> activate#(V) isNeList#(V) -> isPalListKind#(activate(V)) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal#(V) -> activate#(V) isNePal#(V) -> isPalListKind#(activate(V)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) isNePal#(n____(I,__(P,I))) -> activate#(I) isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal#(V) -> activate#(V) isPal#(V) -> isPalListKind#(activate(V)) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) isPalListKind#(n____(V1,V2)) -> activate#(V2) isPalListKind#(n____(V1,V2)) -> activate#(V1) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(X1,X2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) activate#(n__and(X1,X2)) -> and#(X1,X2) activate#(n__a()) -> a#() activate#(n__e()) -> e#() activate#(n__i()) -> i#() activate#(n__o()) -> o#() activate#(n__u()) -> u#() TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and( isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X graph: isPal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isPal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) -> U71#(tt(),V) -> U72#(isNePal(activate(V))) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) -> U71#(tt(),V) -> isNePal#(activate(V)) isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) -> U71#(tt(),V) -> activate#(V) isPal#(V) -> activate#(V) -> activate#(n__u()) -> u#() isPal#(V) -> activate#(V) -> activate#(n__o()) -> o#() isPal#(V) -> activate#(V) -> activate#(n__i()) -> i#() isPal#(V) -> activate#(V) -> activate#(n__e()) -> e#() isPal#(V) -> activate#(V) -> activate#(n__a()) -> a#() isPal#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isPal#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__u()) -> u#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__o()) -> o#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__i()) -> i#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__e()) -> e#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__a()) -> a#() isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPalListKind#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() and#(tt(),X) -> activate#(X) -> activate#(n__u()) -> u#() and#(tt(),X) -> activate#(X) -> activate#(n__o()) -> o#() and#(tt(),X) -> activate#(X) -> activate#(n__i()) -> i#() and#(tt(),X) -> activate#(X) -> activate#(n__e()) -> e#() and#(tt(),X) -> activate#(X) -> activate#(n__a()) -> a#() and#(tt(),X) -> activate#(X) -> activate#(n__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) and#(tt(),X) -> activate#(X) -> activate#(n____(X1,X2)) -> __#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) -> isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) -> isPal#(V) -> isPalListKind#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) -> isPal#(V) -> activate#(V) isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) -> and#(tt(),X) -> activate#(X) isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) -> and#(tt(),X) -> activate#(X) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__u()) -> u#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__o()) -> o#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__i()) -> i#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__e()) -> e#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__a()) -> a#() isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(P) -> activate#(n__nil()) -> nil#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__u()) -> u#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__o()) -> o#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__i()) -> i#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__e()) -> e#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__a()) -> a#() isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__nil()) -> nil#() isNePal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNePal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNePal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isNePal#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) -> U61#(tt(),V) -> U62#(isQid(activate(V))) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) -> U61#(tt(),V) -> isQid#(activate(V)) isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) -> U61#(tt(),V) -> activate#(V) isNePal#(V) -> activate#(V) -> activate#(n__u()) -> u#() isNePal#(V) -> activate#(V) -> activate#(n__o()) -> o#() isNePal#(V) -> activate#(V) -> activate#(n__i()) -> i#() isNePal#(V) -> activate#(V) -> activate#(n__e()) -> e#() isNePal#(V) -> activate#(V) -> activate#(n__a()) -> a#() isNePal#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNePal#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNePal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNePal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> and#(isQid(activate(I)),n__isPalListKind(activate(I))) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(I) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(P) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(V) -> U61#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(V) -> isPalListKind#(activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) -> isNePal#(V) -> activate#(V) U71#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U71#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U71#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U71#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U71#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U71#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U71#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U71#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U71#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() U61#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U61#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U61#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U61#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U61#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U61#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U61#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U61#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U61#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V1) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V2) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> isPalListKind#(activate(V)) U52#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> activate#(V) U52#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U52#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U52#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> U53#(isList(activate(V2))) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> isList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> activate#(V2) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V1) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V2) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(V) -> isPalListKind#(activate(V)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) -> isNeList#(V) -> activate#(V) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__u()) -> u#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__o()) -> o#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__i()) -> i#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__e()) -> e#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__a()) -> a#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__u()) -> u#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__o()) -> o#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__i()) -> i#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__e()) -> e#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__a()) -> a#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> activate#(V1) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> activate#(V2) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> isPalListKind#(activate(V)) U42#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> activate#(V) U42#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U42#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U42#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> U43#(isNeList(activate(V2))) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> isNeList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> activate#(V2) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> isPalListKind#(activate(V)) U41#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__u()) -> u#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__o()) -> o#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__i()) -> i#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__e()) -> e#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__a()) -> a#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__u()) -> u#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__o()) -> o#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__i()) -> i#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__e()) -> e#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__a()) -> a#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() U31#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U31#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U31#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U31#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U31#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U31#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U31#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U31#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U31#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V1) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V2) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> isPalListKind#(activate(V)) U22#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> activate#(V) U22#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U22#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U22#(tt(),V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U22#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U22#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> activate#(V1) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U21#(tt(),V1,V2) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__u()) -> u#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__o()) -> o#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__i()) -> i#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__e()) -> e#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__a()) -> a#() isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isList#(V) -> activate#(V) -> activate#(n__u()) -> u#() isList#(V) -> activate#(V) -> activate#(n__o()) -> o#() isList#(V) -> activate#(V) -> activate#(n__i()) -> i#() isList#(V) -> activate#(V) -> activate#(n__e()) -> e#() isList#(V) -> activate#(V) -> activate#(n__a()) -> a#() isList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isList#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) -> U11#(tt(),V) -> U12#(isNeList(activate(V))) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) -> U11#(tt(),V) -> isNeList#(activate(V)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) -> U11#(tt(),V) -> activate#(V) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) -> U22#(tt(),V2) -> U23#(isList(activate(V2))) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) -> U22#(tt(),V2) -> isList#(activate(V2)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) -> U22#(tt(),V2) -> activate#(V2) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> isPalListKind#(activate(V)) U21#(tt(),V1,V2) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__u()) -> u#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__o()) -> o#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__i()) -> i#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__e()) -> e#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__a()) -> a#() U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U21#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__u()) -> u#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__o()) -> o#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__i()) -> i#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__e()) -> e#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__a()) -> a#() U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) U21#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> activate#(V1) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> activate#(V2) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> activate#(V1) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__u()) -> u#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__o()) -> o#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__i()) -> i#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__e()) -> e#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__a()) -> a#() isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) isNeList#(V) -> isPalListKind#(activate(V)) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> U32#(isQid(activate(V))) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> isQid#(activate(V)) isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> activate#(V) isNeList#(V) -> activate#(V) -> activate#(n__u()) -> u#() isNeList#(V) -> activate#(V) -> activate#(n__o()) -> o#() isNeList#(V) -> activate#(V) -> activate#(n__i()) -> i#() isNeList#(V) -> activate#(V) -> activate#(n__e()) -> e#() isNeList#(V) -> activate#(V) -> activate#(n__a()) -> a#() isNeList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNeList#(V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) isNeList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isNeList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() activate#(n__and(X1,X2)) -> and#(X1,X2) -> and#(tt(),X) -> activate#(X) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__isPalListKind(X)) -> isPalListKind#(X) -> isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(Y,Z) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> isPalListKind#(activate(V1)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V1) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V2) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(V) -> U31#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(V) -> isPalListKind#(activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) -> isNeList#(V) -> activate#(V) U11#(tt(),V) -> activate#(V) -> activate#(n__u()) -> u#() U11#(tt(),V) -> activate#(V) -> activate#(n__o()) -> o#() U11#(tt(),V) -> activate#(V) -> activate#(n__i()) -> i#() U11#(tt(),V) -> activate#(V) -> activate#(n__e()) -> e#() U11#(tt(),V) -> activate#(V) -> activate#(n__a()) -> a#() U11#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U11#(tt(),V) -> activate#(V) -> activate#(n__isPalListKind(X)) -> isPalListKind#(X) U11#(tt(),V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) U11#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() __#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) -> __#(__(X,Y),Z) -> __#(Y,Z) SCC Processor: #sccs: 4 #rules: 26 #arcs: 382/6084 DPs: U52#(tt(),V2) -> isList#(activate(V2)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Usable Rule Processor: DPs: U52#(tt(),V2) -> isList#(activate(V2)) isList#(V) -> U11#(isPalListKind(activate(V)),activate(V)) U11#(tt(),V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U41#(tt(),V1,V2) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U21#(tt(),V1,V2) -> isList#(activate(V1)) U21#(tt(),V1,V2) -> U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) -> isNeList#(activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U51#(tt(),V1,V2) -> isNeList#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNeList(activate(V1)),activate(V2)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() Matrix Interpretation Processor: dim=1 usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() interpretation: [U52#](x0, x1) = 2x1, [U51#](x0, x1, x2) = x0 + 2x1 + 2x2 + 1/2, [U42#](x0, x1) = 1/2x0 + 2x1 + 1/2, [U41#](x0, x1, x2) = 2x1 + 2x2 + 1, [U22#](x0, x1) = x0 + 2x1, [isList#](x0) = 2x0, [U21#](x0, x1, x2) = 2x1 + 2x2 + 1, [isNeList#](x0) = 2x0, [U11#](x0, x1) = 2x1, [u] = 0, [o] = 2, [i] = 0, [e] = 0, [a] = 1, [n__u] = 0, [n__o] = 2, [n__i] = 0, [n__e] = 0, [n__a] = 1, [n__and](x0, x1) = x1, [n__isPalListKind](x0) = 1/2, [n____](x0, x1) = 2x0 + x1 + 1/2, [n__nil] = 0, [isPalListKind](x0) = 1/2, [and](x0, x1) = x1, [U53](x0) = 3/2x0, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 2x2 + 1, [U43](x0) = 0, [U42](x0, x1) = 3x0 + 3, [U41](x0, x1, x2) = 0, [U32](x0) = 3x0 + 3, [isQid](x0) = 7/2, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 1/2x0 + 1/2, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 0, [isNeList](x0) = 0, [activate](x0) = x0, [U11](x0, x1) = 2x0, [tt] = 0, [nil] = 0, [__](x0, x1) = 2x0 + x1 + 1/2 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)) = 4V1 + 2V2 + 1 >= 2V1 + 2V2 + 1 = U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U41#(tt(),V1,V2) = 2V1 + 2V2 + 1 >= 2V1 = isList#(activate(V1)) isList#(n____(V1,V2)) = 4V1 + 2V2 + 1 >= 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 >= 2V2 = isList#(activate(V2)) U41#(tt(),V1,V2) = 2V1 + 2V2 + 1 >= 2V2 + 1 = U42#(isList(activate(V1)),activate(V2)) U42#(tt(),V2) = 2V2 + 1/2 >= 2V2 = isNeList#(activate(V2)) isNeList#(n____(V1,V2)) = 4V1 + 2V2 + 1 >= 2V1 + 2V2 + 1 = U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U51#(tt(),V1,V2) = 2V1 + 2V2 + 1/2 >= 2V1 = isNeList#(activate(V1)) U51#(tt(),V1,V2) = 2V1 + 2V2 + 1/2 >= 2V2 = U52#(isNeList(activate(V1)),activate(V2)) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 2X1 + X2 + 1/2 >= 2X1 + X2 + 1/2 = __(X1,X2) activate(n__isPalListKind(X)) = 1/2 >= 1/2 = isPalListKind(X) activate(n__and(X1,X2)) = X2 >= X2 = and(X1,X2) activate(n__a()) = 1 >= 1 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X nil() = 0 >= 0 = n__nil() __(__(X,Y),Z) = 4X + 2Y + Z + 3/2 >= 2X + 2Y + Z + 1 = __(X,__(Y,Z)) __(X,nil()) = 2X + 1/2 >= X = X __(nil(),X) = X + 1/2 >= X = X __(X1,X2) = 2X1 + X2 + 1/2 >= 2X1 + X2 + 1/2 = n____(X1,X2) isPalListKind(n__a()) = 1/2 >= 0 = tt() isPalListKind(n__e()) = 1/2 >= 0 = tt() isPalListKind(n__i()) = 1/2 >= 0 = tt() isPalListKind(n__nil()) = 1/2 >= 0 = tt() isPalListKind(n__o()) = 1/2 >= 0 = tt() isPalListKind(n__u()) = 1/2 >= 0 = tt() isPalListKind(n____(V1,V2)) = 1/2 >= 1/2 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = 1/2 >= 1/2 = n__isPalListKind(X) and(tt(),X) = X >= X = activate(X) and(X1,X2) = X2 >= X2 = n__and(X1,X2) a() = 1 >= 1 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 2 >= 2 = n__o() u() = 0 >= 0 = n__u() isList(V) = 1 >= 1 = U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) = 1 >= 0 = tt() isList(n____(V1,V2)) = 1 >= 1 = U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) U11(tt(),V) = 0 >= 0 = U12(isNeList(activate(V))) U12(tt()) = 0 >= 0 = tt() isNeList(V) = 0 >= 0 = U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) = 0 >= 0 = U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(n____(V1,V2)) = 0 >= 2V2 + 1 = U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) U31(tt(),V) = 0 >= 27/2 = U32(isQid(activate(V))) U32(tt()) = 3 >= 0 = tt() isQid(n__a()) = 7/2 >= 0 = tt() isQid(n__e()) = 7/2 >= 0 = tt() isQid(n__i()) = 7/2 >= 0 = tt() isQid(n__o()) = 7/2 >= 0 = tt() isQid(n__u()) = 7/2 >= 0 = tt() U41(tt(),V1,V2) = 0 >= 6 = U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) = 3 >= 0 = U43(isNeList(activate(V2))) U43(tt()) = 0 >= 0 = tt() U51(tt(),V1,V2) = 2V2 + 1 >= 1 = U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) = 1 >= 3/2 = U53(isList(activate(V2))) U53(tt()) = 0 >= 0 = tt() U21(tt(),V1,V2) = 1 >= 1 = U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) = 1/2 >= 0 = U23(isList(activate(V2))) U23(tt()) = 0 >= 0 = tt() 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)) 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)) U22#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() 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)) 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)) U22#(tt(),V2) -> isList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isList(activate(V1)),activate(V2)) 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,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X SCC Processor: #sccs: 1 #rules: 3 #arcs: 24/81 DPs: 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)) U22#(tt(),V2) -> isList#(activate(V2)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Usable Rule Processor: DPs: 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)) U22#(tt(),V2) -> isList#(activate(V2)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() Matrix Interpretation Processor: dim=1 usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() interpretation: [U22#](x0, x1) = 2x0 + x1 + 2, [isList#](x0) = x0, [U21#](x0, x1, x2) = x1 + x2 + 4, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [n__u] = 0, [n__o] = 0, [n__i] = 0, [n__e] = 0, [n__a] = 0, [n__and](x0, x1) = 2x0 + x1 + 6, [n__isPalListKind](x0) = 2x0 + 1, [n____](x0, x1) = 2x0 + x1 + 4, [n__nil] = 0, [isPalListKind](x0) = 2x0 + 1, [and](x0, x1) = 2x0 + x1 + 6, [U53](x0) = 2, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 2x0 + 4x1 + 2, [U43](x0) = 0, [U42](x0, x1) = 2x1 + 6, [U41](x0, x1, x2) = 2, [U32](x0) = 4x0 + 5, [isQid](x0) = 2, [U31](x0, x1) = 3x0 + 2x1 + 1, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 0, [isNeList](x0) = 0, [activate](x0) = x0, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [__](x0, x1) = 2x0 + x1 + 4 orientation: isList#(n____(V1,V2)) = 2V1 + V2 + 4 >= V1 + V2 + 4 = U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U21#(tt(),V1,V2) = V1 + V2 + 4 >= V2 + 4 = U22#(isList(activate(V1)),activate(V2)) U22#(tt(),V2) = V2 + 2 >= V2 = isList#(activate(V2)) activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,X2) activate(n__isPalListKind(X)) = 2X + 1 >= 2X + 1 = isPalListKind(X) activate(n__and(X1,X2)) = 2X1 + X2 + 6 >= 2X1 + X2 + 6 = and(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X nil() = 0 >= 0 = n__nil() __(__(X,Y),Z) = 4X + 2Y + Z + 12 >= 2X + 2Y + Z + 8 = __(X,__(Y,Z)) __(X,nil()) = 2X + 4 >= X = X __(nil(),X) = X + 4 >= X = X __(X1,X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = n____(X1,X2) isPalListKind(n__a()) = 1 >= 0 = tt() isPalListKind(n__e()) = 1 >= 0 = tt() isPalListKind(n__i()) = 1 >= 0 = tt() isPalListKind(n__nil()) = 1 >= 0 = tt() isPalListKind(n__o()) = 1 >= 0 = tt() isPalListKind(n__u()) = 1 >= 0 = tt() isPalListKind(n____(V1,V2)) = 4V1 + 2V2 + 9 >= 4V1 + 2V2 + 9 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = 2X + 1 >= 2X + 1 = n__isPalListKind(X) and(tt(),X) = X + 6 >= X = activate(X) and(X1,X2) = 2X1 + X2 + 6 >= 2X1 + X2 + 6 = n__and(X1,X2) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() isList(V) = 1 >= 0 = U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) = 1 >= 0 = tt() isList(n____(V1,V2)) = 1 >= 0 = U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) U11(tt(),V) = 0 >= 0 = U12(isNeList(activate(V))) U12(tt()) = 0 >= 0 = tt() isNeList(V) = 0 >= 8V + 4 = U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) = 0 >= 2 = U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) isNeList(n____(V1,V2)) = 0 >= 12V1 + 4V2 + 20 = U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate ( V1), activate(V2)) U31(tt(),V) = 2V + 1 >= 13 = U32(isQid(activate(V))) U32(tt()) = 5 >= 0 = tt() 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() U41(tt(),V1,V2) = 2 >= 2V2 + 6 = U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) = 2V2 + 6 >= 0 = U43(isNeList(activate(V2))) U43(tt()) = 0 >= 0 = tt() U51(tt(),V1,V2) = 4V1 + 2 >= 0 = U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) = 0 >= 2 = U53(isList(activate(V2))) U53(tt()) = 2 >= 0 = tt() U21(tt(),V1,V2) = 0 >= 0 = U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) = 0 >= 0 = U23(isList(activate(V2))) U23(tt()) = 0 >= 0 = tt() problem: DPs: 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)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() Restore Modifier: DPs: 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)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))), n__and(isPal(activate(P)),n__isPalListKind(activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X SCC Processor: #sccs: 0 #rules: 0 #arcs: 3/4 DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Usable Rule Processor: DPs: isPal#(V) -> U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) -> isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) -> isPal#(activate(P)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Arctic Interpretation Processor: dimension: 1 usable rules: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() interpretation: [isPal#](x0) = 2x0, [isNePal#](x0) = x0 + 0, [U71#](x0, x1) = x0 + x1, [u] = 0, [o] = 0, [i] = 0, [e] = 1, [a] = 1, [n__u] = 0, [n__o] = 0, [n__i] = 0, [n__e] = 1, [n__a] = 1, [n__and](x0, x1) = x1, [n__isPalListKind](x0) = 1x0, [n____](x0, x1) = 3x0 + x1, [n__nil] = 4, [isPalListKind](x0) = 1x0, [and](x0, x1) = x1, [activate](x0) = x0, [tt] = 0, [nil] = 4, [__](x0, x1) = 3x0 + x1 orientation: isPal#(V) = 2V >= 1V = U71#(isPalListKind(activate(V)),activate(V)) U71#(tt(),V) = V + 0 >= V + 0 = isNePal#(activate(V)) isNePal#(n____(I,__(P,I))) = 3I + 3P + 0 >= 2P = isPal#(activate(P)) activate(n__nil()) = 4 >= 4 = nil() activate(n____(X1,X2)) = 3X1 + X2 >= 3X1 + X2 = __(X1,X2) activate(n__isPalListKind(X)) = 1X >= 1X = isPalListKind(X) activate(n__and(X1,X2)) = X2 >= X2 = and(X1,X2) activate(n__a()) = 1 >= 1 = a() activate(n__e()) = 1 >= 1 = 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() = 4 >= 4 = n__nil() __(__(X,Y),Z) = 6X + 3Y + Z >= 3X + 3Y + Z = __(X,__(Y,Z)) __(X,nil()) = 3X + 4 >= X = X __(nil(),X) = X + 7 >= X = X __(X1,X2) = 3X1 + X2 >= 3X1 + X2 = n____(X1,X2) isPalListKind(n__a()) = 2 >= 0 = tt() isPalListKind(n__e()) = 2 >= 0 = tt() isPalListKind(n__i()) = 1 >= 0 = tt() isPalListKind(n__nil()) = 5 >= 0 = tt() isPalListKind(n__o()) = 1 >= 0 = tt() isPalListKind(n__u()) = 1 >= 0 = tt() isPalListKind(n____(V1,V2)) = 4V1 + 1V2 >= 1V2 = and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) = 1X >= 1X = n__isPalListKind(X) and(tt(),X) = X >= X = activate(X) and(X1,X2) = X2 >= X2 = n__and(X1,X2) a() = 1 >= 1 = n__a() e() = 1 >= 1 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() problem: DPs: U71#(tt(),V) -> isNePal#(activate(V)) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Restore Modifier: DPs: U71#(tt(),V) -> isNePal#(activate(V)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X SCC Processor: #sccs: 0 #rules: 0 #arcs: 3/1 DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Usable Rule Processor: DPs: isPalListKind#(n____(V1,V2)) -> activate#(V2) activate#(n__isPalListKind(X)) -> isPalListKind#(X) isPalListKind#(n____(V1,V2)) -> activate#(V1) activate#(n__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) isPalListKind#(n____(V1,V2)) -> isPalListKind#(activate(V1)) isPalListKind#(n____(V1,V2)) -> and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Semantic Labeling Processor: dimension: 1 usable rules: interpretation: [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [n__u] = 1, [n__o] = 1, [n__i] = 1, [n__e] = 1, [n__a] = 1, [n__and](x0, x1) = x0 + x1 + 1, [n__isPalListKind](x0) = x0, [n____](x0, x1) = x0 + x1 + 1, [n__nil] = 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1 + 1, [activate](x0) = x0, [tt] = 1, [nil] = 1, [__](x0, x1) = x0 + x1 + 1 labeled: isPalListKind# activate# and# __ usable (for model): isPalListKind# n____ activate# n__isPalListKind n__and and# tt activate isPalListKind n__nil nil __ and n__a a n__e e n__i i n__o o n__u u argument filtering: pi(__) = 1 pi(nil) = [] pi(tt) = [] pi(activate) = [] pi(and) = 0 pi(isPalListKind) = [] pi(n__nil) = [] pi(n____) = 1 pi(n__isPalListKind) = 0 pi(n__and) = 1 pi(n__a) = [] pi(n__e) = [] pi(n__i) = [] pi(n__o) = [] pi(n__u) = [] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(activate#) = [] pi(and#) = [] pi(isPalListKind#) = [] precedence: isPalListKind# > and# ~ activate# ~ u ~ o ~ i ~ e ~ a ~ n__u ~ n__o ~ n__i ~ n__e ~ n__a ~ n__and ~ n__isPalListKind ~ n____ ~ n__nil ~ isPalListKind ~ and ~ activate ~ tt ~ nil ~ __ problem: DPs: TRS: activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X nil() -> n__nil() __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X __(X1,X2) -> n____(X1,X2) isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isPalListKind(X) -> n__isPalListKind(X) and(tt(),X) -> activate(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() Qed DPs: __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Subterm Criterion Processor: simple projection: pi(__#) = 0 problem: DPs: TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt(),V) -> U12(isNeList(activate(V))) U12(tt()) -> tt() U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2)) U22(tt(),V2) -> U23(isList(activate(V2))) U23(tt()) -> tt() U31(tt(),V) -> U32(isQid(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNeList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isList(activate(V2))) U53(tt()) -> tt() U61(tt(),V) -> U62(isQid(activate(V))) U62(tt()) -> tt() U71(tt(),V) -> U72(isNePal(activate(V))) U72(tt()) -> tt() and(tt(),X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)),activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)),activate(V)) isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))), activate(V1),activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)),activate(V)) isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and (isPal(activate(P)), n__isPalListKind (activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)),activate(V)) isPal(n__nil()) -> tt() isPalListKind(n__a()) -> tt() isPalListKind(n__e()) -> tt() isPalListKind(n__i()) -> tt() isPalListKind(n__nil()) -> tt() isPalListKind(n__o()) -> tt() isPalListKind(n__u()) -> tt() isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isPalListKind(X) -> n__isPalListKind(X) and(X1,X2) -> n__and(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Qed