YES Problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__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)) U21#(tt(),V2) -> activate#(V2) U21#(tt(),V2) -> isList#(activate(V2)) U21#(tt(),V2) -> U22#(isList(activate(V2))) U41#(tt(),V2) -> activate#(V2) U41#(tt(),V2) -> isNeList#(activate(V2)) U41#(tt(),V2) -> U42#(isNeList(activate(V2))) U51#(tt(),V2) -> activate#(V2) U51#(tt(),V2) -> isList#(activate(V2)) U51#(tt(),V2) -> U52#(isList(activate(V2))) U71#(tt(),P) -> activate#(P) U71#(tt(),P) -> isPal#(activate(P)) U71#(tt(),P) -> U72#(isPal(activate(P))) isList#(V) -> activate#(V) isList#(V) -> isNeList#(activate(V)) isList#(V) -> U11#(isNeList(activate(V))) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) isNeList#(V) -> activate#(V) isNeList#(V) -> isQid#(activate(V)) isNeList#(V) -> U31#(isQid(activate(V))) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) isNePal#(V) -> activate#(V) isNePal#(V) -> isQid#(activate(V)) isNePal#(V) -> U61#(isQid(activate(V))) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> activate#(I) isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(P)) isPal#(V) -> activate#(V) isPal#(V) -> isNePal#(activate(V)) isPal#(V) -> U81#(isNePal(activate(V))) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(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()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__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)) U21#(tt(),V2) -> activate#(V2) U21#(tt(),V2) -> isList#(activate(V2)) U21#(tt(),V2) -> U22#(isList(activate(V2))) U41#(tt(),V2) -> activate#(V2) U41#(tt(),V2) -> isNeList#(activate(V2)) U41#(tt(),V2) -> U42#(isNeList(activate(V2))) U51#(tt(),V2) -> activate#(V2) U51#(tt(),V2) -> isList#(activate(V2)) U51#(tt(),V2) -> U52#(isList(activate(V2))) U71#(tt(),P) -> activate#(P) U71#(tt(),P) -> isPal#(activate(P)) U71#(tt(),P) -> U72#(isPal(activate(P))) isList#(V) -> activate#(V) isList#(V) -> isNeList#(activate(V)) isList#(V) -> U11#(isNeList(activate(V))) isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) isNeList#(V) -> activate#(V) isNeList#(V) -> isQid#(activate(V)) isNeList#(V) -> U31#(isQid(activate(V))) isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) isNePal#(V) -> activate#(V) isNePal#(V) -> isQid#(activate(V)) isNePal#(V) -> U61#(isQid(activate(V))) isNePal#(n____(I,__(P,I))) -> activate#(P) isNePal#(n____(I,__(P,I))) -> activate#(I) isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isNePal#(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(P)) isPal#(V) -> activate#(V) isPal#(V) -> isNePal#(activate(V)) isPal#(V) -> U81#(isNePal(activate(V))) activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(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()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X graph: isNePal#(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(P)) -> U71#(tt(),P) -> U72#(isPal(activate(P))) isNePal#(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(P)) -> U71#(tt(),P) -> isPal#(activate(P)) isNePal#(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(P)) -> U71#(tt(),P) -> activate#(P) 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____(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____(X1,X2)) -> __#(X1,X2) isNePal#(n____(I,__(P,I))) -> activate#(I) -> activate#(n__nil()) -> nil#() 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____(X1,X2)) -> __#(X1,X2) isNePal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(P)) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> isQid#(activate(I)) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(I) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(n____(I,__(P,I))) -> activate#(P) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(V) -> U61#(isQid(activate(V))) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(V) -> isQid#(activate(V)) isPal#(V) -> isNePal#(activate(V)) -> isNePal#(V) -> activate#(V) isPal#(V) -> activate#(V) -> activate#(n__u()) -> u#() isPal#(V) -> activate#(V) -> activate#(n__o()) -> o#() isPal#(V) -> activate#(V) -> activate#(n__i()) -> i#() isPal#(V) -> activate#(V) -> activate#(n__e()) -> e#() isPal#(V) -> activate#(V) -> activate#(n__a()) -> a#() isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isPal#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() U71#(tt(),P) -> isPal#(activate(P)) -> isPal#(V) -> U81#(isNePal(activate(V))) U71#(tt(),P) -> isPal#(activate(P)) -> isPal#(V) -> isNePal#(activate(V)) U71#(tt(),P) -> isPal#(activate(P)) -> isPal#(V) -> activate#(V) U71#(tt(),P) -> activate#(P) -> activate#(n__u()) -> u#() U71#(tt(),P) -> activate#(P) -> activate#(n__o()) -> o#() U71#(tt(),P) -> activate#(P) -> activate#(n__i()) -> i#() U71#(tt(),P) -> activate#(P) -> activate#(n__e()) -> e#() U71#(tt(),P) -> activate#(P) -> activate#(n__a()) -> a#() U71#(tt(),P) -> activate#(P) -> activate#(n____(X1,X2)) -> __#(X1,X2) U71#(tt(),P) -> activate#(P) -> activate#(n__nil()) -> nil#() U51#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) U51#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> isList#(activate(V1)) U51#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V1) U51#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V2) U51#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> U11#(isNeList(activate(V))) U51#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> isNeList#(activate(V)) U51#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> activate#(V) U51#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U51#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U51#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U51#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U51#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U51#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U51#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) -> U51#(tt(),V2) -> U52#(isList(activate(V2))) isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) -> U51#(tt(),V2) -> isList#(activate(V2)) isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) -> U51#(tt(),V2) -> activate#(V2) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(V) -> U31#(isQid(activate(V))) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(V) -> isQid#(activate(V)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) -> isNeList#(V) -> activate#(V) isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) -> U41#(tt(),V2) -> U42#(isNeList(activate(V2))) isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) -> U41#(tt(),V2) -> isNeList#(activate(V2)) isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) -> U41#(tt(),V2) -> activate#(V2) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isList#(activate(V1)) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> U11#(isNeList(activate(V))) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isNeList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(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____(X1,X2)) -> __#(X1,X2) isNeList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() 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____(X1,X2)) -> __#(X1,X2) isNeList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> isList#(activate(V1)) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> activate#(V1) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(n____(V1,V2)) -> activate#(V2) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> U31#(isQid(activate(V))) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> isQid#(activate(V)) U41#(tt(),V2) -> isNeList#(activate(V2)) -> isNeList#(V) -> activate#(V) U41#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U41#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U41#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U41#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U41#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U41#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U41#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V1) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(n____(V1,V2)) -> activate#(V2) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> U11#(isNeList(activate(V))) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> isNeList#(activate(V)) isList#(n____(V1,V2)) -> isList#(activate(V1)) -> isList#(V) -> activate#(V) isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__u()) -> u#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__o()) -> o#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__i()) -> i#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__e()) -> e#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n__a()) -> a#() isList#(n____(V1,V2)) -> activate#(V2) -> activate#(n____(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____(X1,X2)) -> __#(X1,X2) isList#(n____(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) -> U21#(tt(),V2) -> U22#(isList(activate(V2))) isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) -> U21#(tt(),V2) -> isList#(activate(V2)) isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) -> U21#(tt(),V2) -> activate#(V2) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V1) isList#(V) -> isNeList#(activate(V)) -> isNeList#(n____(V1,V2)) -> activate#(V2) isList#(V) -> isNeList#(activate(V)) -> isNeList#(V) -> U31#(isQid(activate(V))) isList#(V) -> isNeList#(activate(V)) -> isNeList#(V) -> isQid#(activate(V)) isList#(V) -> isNeList#(activate(V)) -> isNeList#(V) -> activate#(V) isList#(V) -> activate#(V) -> activate#(n__u()) -> u#() isList#(V) -> activate#(V) -> activate#(n__o()) -> o#() isList#(V) -> activate#(V) -> activate#(n__i()) -> i#() isList#(V) -> activate#(V) -> activate#(n__e()) -> e#() isList#(V) -> activate#(V) -> activate#(n__a()) -> a#() isList#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> __#(X1,X2) isList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) activate#(n____(X1,X2)) -> __#(X1,X2) -> __#(__(X,Y),Z) -> __#(Y,Z) U21#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) U21#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> isList#(activate(V1)) U21#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V1) U21#(tt(),V2) -> isList#(activate(V2)) -> isList#(n____(V1,V2)) -> activate#(V2) U21#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> U11#(isNeList(activate(V))) U21#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> isNeList#(activate(V)) U21#(tt(),V2) -> isList#(activate(V2)) -> isList#(V) -> activate#(V) U21#(tt(),V2) -> activate#(V2) -> activate#(n__u()) -> u#() U21#(tt(),V2) -> activate#(V2) -> activate#(n__o()) -> o#() U21#(tt(),V2) -> activate#(V2) -> activate#(n__i()) -> i#() U21#(tt(),V2) -> activate#(V2) -> activate#(n__e()) -> e#() U21#(tt(),V2) -> activate#(V2) -> activate#(n__a()) -> a#() U21#(tt(),V2) -> activate#(V2) -> activate#(n____(X1,X2)) -> __#(X1,X2) U21#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() __#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(Y,Z) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z)) __#(__(X,Y),Z) -> __#(X,__(Y,Z)) -> __#(__(X,Y),Z) -> __#(Y,Z) SCC Processor: #sccs: 3 #rules: 15 #arcs: 181/2209 DPs: U51#(tt(),V2) -> isList#(activate(V2)) isList#(V) -> isNeList#(activate(V)) isNeList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> isList#(activate(V1)) isList#(n____(V1,V2)) -> U21#(isList(activate(V1)),activate(V2)) U21#(tt(),V2) -> isList#(activate(V2)) isNeList#(n____(V1,V2)) -> U41#(isList(activate(V1)),activate(V2)) U41#(tt(),V2) -> isNeList#(activate(V2)) isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) isNeList#(n____(V1,V2)) -> U51#(isNeList(activate(V1)),activate(V2)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [U51#](x0, x1) = x1 + 2, [isNeList#](x0) = x0, [U41#](x0, x1) = x1 + 5, [isList#](x0) = x0 + 1, [U21#](x0, x1) = x1 + 4, [u] = 0, [o] = 1, [i] = 0, [e] = 0, [a] = 0, [n__u] = 0, [n__o] = 1, [n__i] = 0, [n__e] = 0, [n__a] = 0, [isNePal](x0) = 2, [isQid](x0) = 2x0, [n____](x0, x1) = x0 + x1 + 6, [n__nil] = 0, [U81](x0) = 4, [U72](x0) = 1, [isPal](x0) = 4, [U71](x0, x1) = 1, [U61](x0) = 2, [U52](x0) = x0 + 4, [U51](x0, x1) = 2x1 + 5, [U42](x0) = 0, [isNeList](x0) = 2x0 + 2, [U41](x0, x1) = 2x0, [U31](x0) = x0 + 2, [U22](x0) = 2, [isList](x0) = x0 + 1, [activate](x0) = x0, [U21](x0, x1) = x0 + 2, [U11](x0) = 1, [tt] = 0, [nil] = 0, [__](x0, x1) = x0 + x1 + 6 orientation: U51#(tt(),V2) = V2 + 2 >= V2 + 1 = isList#(activate(V2)) isList#(V) = V + 1 >= V = isNeList#(activate(V)) isNeList#(n____(V1,V2)) = V1 + V2 + 6 >= V1 + 1 = isList#(activate(V1)) isList#(n____(V1,V2)) = V1 + V2 + 7 >= V1 + 1 = isList#(activate(V1)) isList#(n____(V1,V2)) = V1 + V2 + 7 >= V2 + 4 = U21#(isList(activate(V1)),activate(V2)) U21#(tt(),V2) = V2 + 4 >= V2 + 1 = isList#(activate(V2)) isNeList#(n____(V1,V2)) = V1 + V2 + 6 >= V2 + 5 = U41#(isList(activate(V1)),activate(V2)) U41#(tt(),V2) = V2 + 5 >= V2 = isNeList#(activate(V2)) isNeList#(n____(V1,V2)) = V1 + V2 + 6 >= V1 = isNeList#(activate(V1)) isNeList#(n____(V1,V2)) = V1 + V2 + 6 >= V2 + 2 = U51#(isNeList(activate(V1)),activate(V2)) __(__(X,Y),Z) = X + Y + Z + 12 >= X + Y + Z + 12 = __(X,__(Y,Z)) __(X,nil()) = X + 6 >= X = X __(nil(),X) = X + 6 >= X = X U11(tt()) = 1 >= 0 = tt() U21(tt(),V2) = 2 >= 2 = U22(isList(activate(V2))) U22(tt()) = 2 >= 0 = tt() U31(tt()) = 2 >= 0 = tt() U41(tt(),V2) = 0 >= 0 = U42(isNeList(activate(V2))) U42(tt()) = 0 >= 0 = tt() U51(tt(),V2) = 2V2 + 5 >= V2 + 5 = U52(isList(activate(V2))) U52(tt()) = 4 >= 0 = tt() U61(tt()) = 2 >= 0 = tt() U71(tt(),P) = 1 >= 1 = U72(isPal(activate(P))) U72(tt()) = 1 >= 0 = tt() U81(tt()) = 4 >= 0 = tt() isList(V) = V + 1 >= 1 = U11(isNeList(activate(V))) isList(n__nil()) = 1 >= 0 = tt() isList(n____(V1,V2)) = V1 + V2 + 7 >= V1 + 3 = U21(isList(activate(V1)),activate(V2)) isNeList(V) = 2V + 2 >= 2V + 2 = U31(isQid(activate(V))) isNeList(n____(V1,V2)) = 2V1 + 2V2 + 14 >= 2V1 + 2 = U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) = 2V1 + 2V2 + 14 >= 2V2 + 5 = U51(isNeList(activate(V1)),activate(V2)) isNePal(V) = 2 >= 2 = U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) = 2 >= 1 = U71(isQid(activate(I)),activate(P)) isPal(V) = 4 >= 4 = U81(isNePal(activate(V))) isPal(n__nil()) = 4 >= 0 = tt() isQid(n__a()) = 0 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 0 >= 0 = tt() isQid(n__o()) = 2 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = X1 + X2 + 6 >= X1 + X2 + 6 = n____(X1,X2) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 1 >= 1 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = X1 + X2 + 6 >= X1 + X2 + 6 = __(X1,X2) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 1 >= 1 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X problem: DPs: TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Qed DPs: isNePal#(n____(I,__(P,I))) -> U71#(isQid(activate(I)),activate(P)) U71#(tt(),P) -> isPal#(activate(P)) isPal#(V) -> isNePal#(activate(V)) TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [isNePal#](x0) = x0 + 1/2, [isPal#](x0) = x0 + 1, [U71#](x0, x1) = 3x0 + x1, [u] = 1, [o] = 2, [i] = 2, [e] = 1, [a] = 1, [n__u] = 1, [n__o] = 2, [n__i] = 2, [n__e] = 1, [n__a] = 1, [isNePal](x0) = x0 + 1/2, [isQid](x0) = 1/2x0, [n____](x0, x1) = 3x0 + x1 + 2, [n__nil] = 2, [U81](x0) = 3x0 + 1, [U72](x0) = 1, [isPal](x0) = 7/2x0 + 5/2, [U71](x0, x1) = 2x0 + x1, [U61](x0) = 2x0, [U52](x0) = 5/2, [U51](x0, x1) = 1/2x1 + 5/2, [U42](x0) = 1, [isNeList](x0) = 5/2x0 + 2, [U41](x0, x1) = 2x0 + 1/2, [U31](x0) = 2, [U22](x0) = 1, [isList](x0) = 7/2x0 + 3, [activate](x0) = x0, [U21](x0, x1) = 1, [U11](x0) = 1/2, [tt] = 1/2, [nil] = 2, [__](x0, x1) = 3x0 + x1 + 2 orientation: isNePal#(n____(I,__(P,I))) = 4I + 3P + 9/2 >= 3/2I + P = U71#(isQid(activate(I)),activate(P)) U71#(tt(),P) = P + 3/2 >= P + 1 = isPal#(activate(P)) isPal#(V) = V + 1 >= V + 1/2 = isNePal#(activate(V)) __(__(X,Y),Z) = 9X + 3Y + Z + 8 >= 3X + 3Y + Z + 4 = __(X,__(Y,Z)) __(X,nil()) = 3X + 4 >= X = X __(nil(),X) = X + 8 >= X = X U11(tt()) = 1/2 >= 1/2 = tt() U21(tt(),V2) = 1 >= 1 = U22(isList(activate(V2))) U22(tt()) = 1 >= 1/2 = tt() U31(tt()) = 2 >= 1/2 = tt() U41(tt(),V2) = 3/2 >= 1 = U42(isNeList(activate(V2))) U42(tt()) = 1 >= 1/2 = tt() U51(tt(),V2) = 1/2V2 + 5/2 >= 5/2 = U52(isList(activate(V2))) U52(tt()) = 5/2 >= 1/2 = tt() U61(tt()) = 1 >= 1/2 = tt() U71(tt(),P) = P + 1 >= 1 = U72(isPal(activate(P))) U72(tt()) = 1 >= 1/2 = tt() U81(tt()) = 5/2 >= 1/2 = tt() isList(V) = 7/2V + 3 >= 1/2 = U11(isNeList(activate(V))) isList(n__nil()) = 10 >= 1/2 = tt() isList(n____(V1,V2)) = 21/2V1 + 7/2V2 + 10 >= 1 = U21(isList(activate(V1)),activate(V2)) isNeList(V) = 5/2V + 2 >= 2 = U31(isQid(activate(V))) isNeList(n____(V1,V2)) = 15/2V1 + 5/2V2 + 7 >= 7V1 + 13/2 = U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) = 15/2V1 + 5/2V2 + 7 >= 1/2V2 + 5/2 = U51(isNeList(activate(V1)),activate(V2)) isNePal(V) = V + 1/2 >= V = U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) = 4I + 3P + 9/2 >= I + P = U71(isQid(activate(I)),activate(P)) isPal(V) = 7/2V + 5/2 >= 3V + 5/2 = U81(isNePal(activate(V))) isPal(n__nil()) = 19/2 >= 1/2 = tt() isQid(n__a()) = 1/2 >= 1/2 = tt() isQid(n__e()) = 1/2 >= 1/2 = tt() isQid(n__i()) = 1 >= 1/2 = tt() isQid(n__o()) = 1 >= 1/2 = tt() isQid(n__u()) = 1/2 >= 1/2 = tt() nil() = 2 >= 2 = n__nil() __(X1,X2) = 3X1 + X2 + 2 >= 3X1 + X2 + 2 = n____(X1,X2) a() = 1 >= 1 = n__a() e() = 1 >= 1 = n__e() i() = 2 >= 2 = n__i() o() = 2 >= 2 = n__o() u() = 1 >= 1 = n__u() activate(n__nil()) = 2 >= 2 = nil() activate(n____(X1,X2)) = 3X1 + X2 + 2 >= 3X1 + X2 + 2 = __(X1,X2) activate(n__a()) = 1 >= 1 = a() activate(n__e()) = 1 >= 1 = e() activate(n__i()) = 2 >= 2 = i() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 1 >= 1 = u() activate(X) = X >= X = X problem: DPs: TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X 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()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [__#](x0, x1) = 3/2x0 + 7/2, [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, [isNePal](x0) = 1/2x0 + 5/2, [isQid](x0) = 1/2x0, [n____](x0, x1) = 2x0 + x1 + 3, [n__nil] = 0, [U81](x0) = 0, [U72](x0) = 2, [isPal](x0) = 0, [U71](x0, x1) = 2x0 + x1 + 7/2, [U61](x0) = x0 + 2, [U52](x0) = 0, [U51](x0, x1) = 2x0 + 1/2x1, [U42](x0) = 1, [isNeList](x0) = 1/2x0, [U41](x0, x1) = 1/2x1 + 1, [U31](x0) = 0, [U22](x0) = 0, [isList](x0) = 3, [activate](x0) = x0 + 1, [U21](x0, x1) = 3, [U11](x0) = 3/2, [tt] = 0, [nil] = 1/2, [__](x0, x1) = 2x0 + x1 + 3 orientation: __#(__(X,Y),Z) = 3X + 3/2Y + 8 >= 3/2Y + 7/2 = __#(Y,Z) __#(__(X,Y),Z) = 3X + 3/2Y + 8 >= 3/2X + 7/2 = __#(X,__(Y,Z)) __(__(X,Y),Z) = 4X + 2Y + Z + 9 >= 2X + 2Y + Z + 6 = __(X,__(Y,Z)) __(X,nil()) = 2X + 7/2 >= X = X __(nil(),X) = X + 4 >= X = X U11(tt()) = 3/2 >= 0 = tt() U21(tt(),V2) = 3 >= 0 = U22(isList(activate(V2))) U22(tt()) = 0 >= 0 = tt() U31(tt()) = 0 >= 0 = tt() U41(tt(),V2) = 1/2V2 + 1 >= 1 = U42(isNeList(activate(V2))) U42(tt()) = 1 >= 0 = tt() U51(tt(),V2) = 1/2V2 >= 0 = U52(isList(activate(V2))) U52(tt()) = 0 >= 0 = tt() U61(tt()) = 2 >= 0 = tt() U71(tt(),P) = P + 7/2 >= 2 = U72(isPal(activate(P))) U72(tt()) = 2 >= 0 = tt() U81(tt()) = 0 >= 0 = tt() isList(V) = 3 >= 3/2 = U11(isNeList(activate(V))) isList(n__nil()) = 3 >= 0 = tt() isList(n____(V1,V2)) = 3 >= 3 = U21(isList(activate(V1)),activate(V2)) isNeList(V) = 1/2V >= 0 = U31(isQid(activate(V))) isNeList(n____(V1,V2)) = V1 + 1/2V2 + 3/2 >= 1/2V2 + 3/2 = U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) = V1 + 1/2V2 + 3/2 >= V1 + 1/2V2 + 3/2 = U51(isNeList(activate(V1)),activate(V2)) isNePal(V) = 1/2V + 5/2 >= 1/2V + 5/2 = U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) = 3/2I + P + 11/2 >= I + P + 11/2 = U71(isQid(activate(I)),activate(P)) isPal(V) = 0 >= 0 = U81(isNePal(activate(V))) isPal(n__nil()) = 0 >= 0 = tt() isQid(n__a()) = 0 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 0 >= 0 = tt() isQid(n__o()) = 0 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() nil() = 1/2 >= 0 = n__nil() __(X1,X2) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = n____(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() activate(n__nil()) = 1 >= 1/2 = nil() activate(n____(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 3 = __(X1,X2) activate(n__a()) = 1 >= 0 = a() activate(n__e()) = 1 >= 0 = e() activate(n__i()) = 1 >= 0 = i() activate(n__o()) = 1 >= 0 = o() activate(n__u()) = 1 >= 0 = u() activate(X) = X + 1 >= X = X problem: DPs: TRS: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) 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__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Qed