MAYBE Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U11(tt(),V)) -> isNeList#(V) active#(U11(tt(),V)) -> U12#(isNeList(V)) active#(U21(tt(),V1,V2)) -> isList#(V1) active#(U21(tt(),V1,V2)) -> U22#(isList(V1),V2) active#(U22(tt(),V2)) -> isList#(V2) active#(U22(tt(),V2)) -> U23#(isList(V2)) active#(U31(tt(),V)) -> isQid#(V) active#(U31(tt(),V)) -> U32#(isQid(V)) active#(U41(tt(),V1,V2)) -> isList#(V1) active#(U41(tt(),V1,V2)) -> U42#(isList(V1),V2) active#(U42(tt(),V2)) -> isNeList#(V2) active#(U42(tt(),V2)) -> U43#(isNeList(V2)) active#(U51(tt(),V1,V2)) -> isNeList#(V1) active#(U51(tt(),V1,V2)) -> U52#(isNeList(V1),V2) active#(U52(tt(),V2)) -> isList#(V2) active#(U52(tt(),V2)) -> U53#(isList(V2)) active#(U61(tt(),V)) -> isQid#(V) active#(U61(tt(),V)) -> U62#(isQid(V)) active#(U71(tt(),V)) -> isNePal#(V) active#(U71(tt(),V)) -> U72#(isNePal(V)) active#(isList(V)) -> isPalListKind#(V) active#(isList(V)) -> U11#(isPalListKind(V),V) active#(isList(__(V1,V2))) -> isPalListKind#(V2) active#(isList(__(V1,V2))) -> isPalListKind#(V1) active#(isList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isList(__(V1,V2))) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(V)) -> isPalListKind#(V) active#(isNeList(V)) -> U31#(isPalListKind(V),V) active#(isNeList(__(V1,V2))) -> isPalListKind#(V2) active#(isNeList(__(V1,V2))) -> isPalListKind#(V1) active#(isNeList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isNeList(__(V1,V2))) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(__(V1,V2))) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNePal(V)) -> isPalListKind#(V) active#(isNePal(V)) -> U61#(isPalListKind(V),V) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(P) active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(isNePal(__(I,__(P,I)))) -> and#(isPal(P),isPalListKind(P)) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(I) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPalListKind(I)) active#(isNePal(__(I,__(P,I)))) -> and#(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) active#(isPal(V)) -> isPalListKind#(V) active#(isPal(V)) -> U71#(isPalListKind(V),V) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V2) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1) active#(isPalListKind(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X1,X2)) -> active#(X1) active#(U11(X1,X2)) -> U11#(active(X1),X2) active#(U12(X)) -> active#(X) active#(U12(X)) -> U12#(active(X)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2)) -> active#(X1) active#(U22(X1,X2)) -> U22#(active(X1),X2) active#(U23(X)) -> active#(X) active#(U23(X)) -> U23#(active(X)) active#(U31(X1,X2)) -> active#(X1) active#(U31(X1,X2)) -> U31#(active(X1),X2) active#(U32(X)) -> active#(X) active#(U32(X)) -> U32#(active(X)) active#(U41(X1,X2,X3)) -> active#(X1) active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3) active#(U42(X1,X2)) -> active#(X1) active#(U42(X1,X2)) -> U42#(active(X1),X2) active#(U43(X)) -> active#(X) active#(U43(X)) -> U43#(active(X)) active#(U51(X1,X2,X3)) -> active#(X1) active#(U51(X1,X2,X3)) -> U51#(active(X1),X2,X3) active#(U52(X1,X2)) -> active#(X1) active#(U52(X1,X2)) -> U52#(active(X1),X2) active#(U53(X)) -> active#(X) active#(U53(X)) -> U53#(active(X)) active#(U61(X1,X2)) -> active#(X1) active#(U61(X1,X2)) -> U61#(active(X1),X2) active#(U62(X)) -> active#(X) active#(U62(X)) -> U62#(active(X)) active#(U71(X1,X2)) -> active#(X1) active#(U71(X1,X2)) -> U71#(active(X1),X2) active#(U72(X)) -> active#(X) active#(U72(X)) -> U72#(active(X)) active#(and(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> and#(active(X1),X2) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U12#(mark(X)) -> U12#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2) -> U22#(X1,X2) U23#(mark(X)) -> U23#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U32#(mark(X)) -> U32#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U42#(mark(X1),X2) -> U42#(X1,X2) U43#(mark(X)) -> U43#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U52#(mark(X1),X2) -> U52#(X1,X2) U53#(mark(X)) -> U53#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) and#(mark(X1),X2) -> and#(X1,X2) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X1,X2)) -> proper#(X2) proper#(U11(X1,X2)) -> proper#(X1) proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2)) proper#(U12(X)) -> proper#(X) proper#(U12(X)) -> U12#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2)) -> proper#(X2) proper#(U22(X1,X2)) -> proper#(X1) proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2)) proper#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(U23(X)) -> proper#(X) proper#(U23(X)) -> U23#(proper(X)) proper#(U31(X1,X2)) -> proper#(X2) proper#(U31(X1,X2)) -> proper#(X1) proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2)) proper#(U32(X)) -> proper#(X) proper#(U32(X)) -> U32#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3)) proper#(U42(X1,X2)) -> proper#(X2) proper#(U42(X1,X2)) -> proper#(X1) proper#(U42(X1,X2)) -> U42#(proper(X1),proper(X2)) proper#(U43(X)) -> proper#(X) proper#(U43(X)) -> U43#(proper(X)) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U51(X1,X2,X3)) -> U51#(proper(X1),proper(X2),proper(X3)) proper#(U52(X1,X2)) -> proper#(X2) proper#(U52(X1,X2)) -> proper#(X1) proper#(U52(X1,X2)) -> U52#(proper(X1),proper(X2)) proper#(U53(X)) -> proper#(X) proper#(U53(X)) -> U53#(proper(X)) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2)) proper#(U62(X)) -> proper#(X) proper#(U62(X)) -> U62#(proper(X)) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) proper#(U72(X)) -> proper#(X) proper#(U72(X)) -> U72#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isPalListKind(X)) -> proper#(X) proper#(isPalListKind(X)) -> isPalListKind#(proper(X)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X1),ok(X2)) -> U11#(X1,X2) U12#(ok(X)) -> U12#(X) isNeList#(ok(X)) -> isNeList#(X) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2)) -> U22#(X1,X2) isList#(ok(X)) -> isList#(X) U23#(ok(X)) -> U23#(X) U31#(ok(X1),ok(X2)) -> U31#(X1,X2) U32#(ok(X)) -> U32#(X) isQid#(ok(X)) -> isQid#(X) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) U42#(ok(X1),ok(X2)) -> U42#(X1,X2) U43#(ok(X)) -> U43#(X) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) U52#(ok(X1),ok(X2)) -> U52#(X1,X2) U53#(ok(X)) -> U53#(X) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) U62#(ok(X)) -> U62#(X) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(ok(X)) -> U72#(X) isNePal#(ok(X)) -> isNePal#(X) and#(ok(X1),ok(X2)) -> and#(X1,X2) isPalListKind#(ok(X)) -> isPalListKind#(X) isPal#(ok(X)) -> isPal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(U11(tt(),V)) -> isNeList#(V) active#(U11(tt(),V)) -> U12#(isNeList(V)) active#(U21(tt(),V1,V2)) -> isList#(V1) active#(U21(tt(),V1,V2)) -> U22#(isList(V1),V2) active#(U22(tt(),V2)) -> isList#(V2) active#(U22(tt(),V2)) -> U23#(isList(V2)) active#(U31(tt(),V)) -> isQid#(V) active#(U31(tt(),V)) -> U32#(isQid(V)) active#(U41(tt(),V1,V2)) -> isList#(V1) active#(U41(tt(),V1,V2)) -> U42#(isList(V1),V2) active#(U42(tt(),V2)) -> isNeList#(V2) active#(U42(tt(),V2)) -> U43#(isNeList(V2)) active#(U51(tt(),V1,V2)) -> isNeList#(V1) active#(U51(tt(),V1,V2)) -> U52#(isNeList(V1),V2) active#(U52(tt(),V2)) -> isList#(V2) active#(U52(tt(),V2)) -> U53#(isList(V2)) active#(U61(tt(),V)) -> isQid#(V) active#(U61(tt(),V)) -> U62#(isQid(V)) active#(U71(tt(),V)) -> isNePal#(V) active#(U71(tt(),V)) -> U72#(isNePal(V)) active#(isList(V)) -> isPalListKind#(V) active#(isList(V)) -> U11#(isPalListKind(V),V) active#(isList(__(V1,V2))) -> isPalListKind#(V2) active#(isList(__(V1,V2))) -> isPalListKind#(V1) active#(isList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isList(__(V1,V2))) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(V)) -> isPalListKind#(V) active#(isNeList(V)) -> U31#(isPalListKind(V),V) active#(isNeList(__(V1,V2))) -> isPalListKind#(V2) active#(isNeList(__(V1,V2))) -> isPalListKind#(V1) active#(isNeList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(isNeList(__(V1,V2))) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNeList(__(V1,V2))) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) active#(isNePal(V)) -> isPalListKind#(V) active#(isNePal(V)) -> U61#(isPalListKind(V),V) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(P) active#(isNePal(__(I,__(P,I)))) -> isPal#(P) active#(isNePal(__(I,__(P,I)))) -> and#(isPal(P),isPalListKind(P)) active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(I) active#(isNePal(__(I,__(P,I)))) -> isQid#(I) active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPalListKind(I)) active#(isNePal(__(I,__(P,I)))) -> and#(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) active#(isPal(V)) -> isPalListKind#(V) active#(isPal(V)) -> U71#(isPalListKind(V),V) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V2) active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1) active#(isPalListKind(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2)) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X1,X2)) -> active#(X1) active#(U11(X1,X2)) -> U11#(active(X1),X2) active#(U12(X)) -> active#(X) active#(U12(X)) -> U12#(active(X)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2)) -> active#(X1) active#(U22(X1,X2)) -> U22#(active(X1),X2) active#(U23(X)) -> active#(X) active#(U23(X)) -> U23#(active(X)) active#(U31(X1,X2)) -> active#(X1) active#(U31(X1,X2)) -> U31#(active(X1),X2) active#(U32(X)) -> active#(X) active#(U32(X)) -> U32#(active(X)) active#(U41(X1,X2,X3)) -> active#(X1) active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3) active#(U42(X1,X2)) -> active#(X1) active#(U42(X1,X2)) -> U42#(active(X1),X2) active#(U43(X)) -> active#(X) active#(U43(X)) -> U43#(active(X)) active#(U51(X1,X2,X3)) -> active#(X1) active#(U51(X1,X2,X3)) -> U51#(active(X1),X2,X3) active#(U52(X1,X2)) -> active#(X1) active#(U52(X1,X2)) -> U52#(active(X1),X2) active#(U53(X)) -> active#(X) active#(U53(X)) -> U53#(active(X)) active#(U61(X1,X2)) -> active#(X1) active#(U61(X1,X2)) -> U61#(active(X1),X2) active#(U62(X)) -> active#(X) active#(U62(X)) -> U62#(active(X)) active#(U71(X1,X2)) -> active#(X1) active#(U71(X1,X2)) -> U71#(active(X1),X2) active#(U72(X)) -> active#(X) active#(U72(X)) -> U72#(active(X)) active#(and(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> and#(active(X1),X2) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U12#(mark(X)) -> U12#(X) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2) -> U22#(X1,X2) U23#(mark(X)) -> U23#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U32#(mark(X)) -> U32#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U42#(mark(X1),X2) -> U42#(X1,X2) U43#(mark(X)) -> U43#(X) U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U52#(mark(X1),X2) -> U52#(X1,X2) U53#(mark(X)) -> U53#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) and#(mark(X1),X2) -> and#(X1,X2) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X1,X2)) -> proper#(X2) proper#(U11(X1,X2)) -> proper#(X1) proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2)) proper#(U12(X)) -> proper#(X) proper#(U12(X)) -> U12#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2)) -> proper#(X2) proper#(U22(X1,X2)) -> proper#(X1) proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2)) proper#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(U23(X)) -> proper#(X) proper#(U23(X)) -> U23#(proper(X)) proper#(U31(X1,X2)) -> proper#(X2) proper#(U31(X1,X2)) -> proper#(X1) proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2)) proper#(U32(X)) -> proper#(X) proper#(U32(X)) -> U32#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3)) proper#(U42(X1,X2)) -> proper#(X2) proper#(U42(X1,X2)) -> proper#(X1) proper#(U42(X1,X2)) -> U42#(proper(X1),proper(X2)) proper#(U43(X)) -> proper#(X) proper#(U43(X)) -> U43#(proper(X)) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U51(X1,X2,X3)) -> U51#(proper(X1),proper(X2),proper(X3)) proper#(U52(X1,X2)) -> proper#(X2) proper#(U52(X1,X2)) -> proper#(X1) proper#(U52(X1,X2)) -> U52#(proper(X1),proper(X2)) proper#(U53(X)) -> proper#(X) proper#(U53(X)) -> U53#(proper(X)) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2)) proper#(U62(X)) -> proper#(X) proper#(U62(X)) -> U62#(proper(X)) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) proper#(U72(X)) -> proper#(X) proper#(U72(X)) -> U72#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) proper#(and(X1,X2)) -> and#(proper(X1),proper(X2)) proper#(isPalListKind(X)) -> proper#(X) proper#(isPalListKind(X)) -> isPalListKind#(proper(X)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X1),ok(X2)) -> U11#(X1,X2) U12#(ok(X)) -> U12#(X) isNeList#(ok(X)) -> isNeList#(X) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2)) -> U22#(X1,X2) isList#(ok(X)) -> isList#(X) U23#(ok(X)) -> U23#(X) U31#(ok(X1),ok(X2)) -> U31#(X1,X2) U32#(ok(X)) -> U32#(X) isQid#(ok(X)) -> isQid#(X) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) U42#(ok(X1),ok(X2)) -> U42#(X1,X2) U43#(ok(X)) -> U43#(X) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) U52#(ok(X1),ok(X2)) -> U52#(X1,X2) U53#(ok(X)) -> U53#(X) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) U62#(ok(X)) -> U62#(X) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(ok(X)) -> U72#(X) isNePal#(ok(X)) -> isNePal#(X) and#(ok(X1),ok(X2)) -> and#(X1,X2) isPalListKind#(ok(X)) -> isPalListKind#(X) isPal#(ok(X)) -> isPal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: ... SCC Processor: #sccs: 28 #rules: 107 #arcs: 4792/41209 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) active#(U11(X1,X2)) -> active#(X1) active#(U12(X)) -> active#(X) active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2)) -> active#(X1) active#(U23(X)) -> active#(X) active#(U31(X1,X2)) -> active#(X1) active#(U32(X)) -> active#(X) active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2)) -> active#(X1) active#(U43(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2)) -> active#(X1) active#(U53(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X)) -> active#(X) active#(U71(X1,X2)) -> active#(X1) active#(U72(X)) -> active#(X) active#(and(X1,X2)) -> active#(X1) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = x0 + 1, [and](x0, x1) = x0 + x1, [U72](x0) = x0 + 1, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0 + 1, [isQid](x0) = 0, [U31](x0, x1) = x0 + 1, [U23](x0) = x0 + 1, [U22](x0, x1) = x0 + 1, [isList](x0) = 0, [U21](x0, x1, x2) = x0 + 1, [U12](x0) = x0 + 1, [isNeList](x0) = x0, [U11](x0, x1) = x0 + 1, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active#(__(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(__(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2) active#(U11(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U12(X)) = X + 2 >= X + 1 = active#(X) active#(U21(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U22(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U23(X)) = X + 2 >= X + 1 = active#(X) active#(U31(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U32(X)) = X + 2 >= X + 1 = active#(X) active#(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(X1) active#(U42(X1,X2)) = X1 + 1 >= X1 + 1 = active#(X1) active#(U43(X)) = X + 1 >= X + 1 = active#(X) active#(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(X1) active#(U52(X1,X2)) = X1 + 1 >= X1 + 1 = active#(X1) active#(U53(X)) = X + 1 >= X + 1 = active#(X) active#(U61(X1,X2)) = X1 + 1 >= X1 + 1 = active#(X1) active#(U62(X)) = X + 1 >= X + 1 = active#(X) active#(U71(X1,X2)) = X1 + 1 >= X1 + 1 = active#(X1) active#(U72(X)) = X + 2 >= X + 1 = active#(X) active#(and(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= 0 = mark(X) active(__(nil(),X)) = X + 2 >= 0 = mark(X) active(U11(tt(),V)) = 1 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 0 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 0 = mark(tt()) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = 0 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 0 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 0 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 2 >= 0 = mark(tt()) active(isPalListKind(i())) = 2 >= 0 = mark(tt()) active(isPalListKind(nil())) = 2 >= 0 = mark(tt()) active(isPalListKind(o())) = 2 >= 0 = mark(tt()) active(isPalListKind(u())) = 2 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 >= X1 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X1 >= X1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 >= X1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X1 >= X1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 1 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 1 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 1 >= 0 = mark(U23(X)) U31(mark(X1),X2) = 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 1 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = 0 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = 0 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = 0 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = 0 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 1 >= 0 = mark(U72(X)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2)) -> active#(X1) active#(U43(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U52(X1,X2)) -> active#(X1) active#(U53(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X)) -> active#(X) active#(U71(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> active#(X1) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 1, [o] = 1, [i] = 0, [e] = 0, [a] = 1, [isPal](x0) = 1, [isPalListKind](x0) = 0, [and](x0, x1) = x0, [U72](x0) = 1, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0 + 1, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = 0, [isQid](x0) = x0 + 1, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [isList](x0) = 1, [U21](x0, x1, x2) = 0, [U12](x0) = 0, [isNeList](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = 0 orientation: active#(U41(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U42(X1,X2)) = X1 >= X1 = active#(X1) active#(U43(X)) = X >= X = active#(X) active#(U51(X1,X2,X3)) = X1 >= X1 = active#(X1) active#(U52(X1,X2)) = X1 + 1 >= X1 = active#(X1) active#(U53(X)) = X >= X = active#(X) active#(U61(X1,X2)) = X1 >= X1 = active#(X1) active#(U62(X)) = X >= X = active#(X) active#(U71(X1,X2)) = X1 >= X1 = active#(X1) active#(and(X1,X2)) = X1 >= X1 = active#(X1) active(__(__(X,Y),Z)) = 0 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 0 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = 1 >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 0 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 0 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 0 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 0 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = 0 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 2 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 2 >= 0 = mark(tt()) active(isQid(u())) = 2 >= 0 = mark(tt()) active(__(X1,X2)) = 0 >= 0 = __(active(X1),X2) active(__(X1,X2)) = 0 >= 0 = __(X1,active(X2)) active(U11(X1,X2)) = 0 >= 0 = U11(active(X1),X2) active(U12(X)) = 0 >= 0 = U12(active(X)) active(U21(X1,X2,X3)) = 0 >= 0 = U21(active(X1),X2,X3) active(U22(X1,X2)) = 0 >= 0 = U22(active(X1),X2) active(U23(X)) = 0 >= 0 = U23(active(X)) active(U31(X1,X2)) = 0 >= 0 = U31(active(X1),X2) active(U32(X)) = 0 >= 0 = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 >= X1 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X1 >= X1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X1 >= X1 = U71(active(X1),X2) active(U72(X)) = 1 >= 1 = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = 0 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = 0 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = 0 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = 0 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 1 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 1 >= 1 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = 1 >= 1 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 >= X1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = 0 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 0 >= 0 = ok(U11(X1,X2)) U12(ok(X)) = 0 >= 0 = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = 0 >= 0 = ok(U22(X1,X2)) isList(ok(X)) = 1 >= 1 = ok(isList(X)) U23(ok(X)) = 0 >= 0 = ok(U23(X)) U31(ok(X1),ok(X2)) = 0 >= 0 = ok(U31(X1,X2)) U32(ok(X)) = 0 >= 0 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = 1 >= 1 = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 >= X1 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 1 >= 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(U41(X1,X2,X3)) -> active#(X1) active#(U42(X1,X2)) -> active#(X1) active#(U43(X)) -> active#(X) active#(U51(X1,X2,X3)) -> active#(X1) active#(U53(X)) -> active#(X) active#(U61(X1,X2)) -> active#(X1) active#(U62(X)) -> active#(X) active#(U71(X1,X2)) -> active#(X1) active#(and(X1,X2)) -> active#(X1) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 1, [e] = 0, [a] = 0, [isPal](x0) = 1, [isPalListKind](x0) = 1, [and](x0, x1) = x0 + 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = x0 + 1, [U62](x0) = x0 + 1, [U61](x0, x1) = x0 + 1, [U53](x0) = x0 + 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = x0 + 1, [U43](x0) = x0 + 1, [U42](x0, x1) = x0 + 1, [U41](x0, x1, x2) = x0 + 1, [U32](x0) = 1, [isQid](x0) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [U22](x0, x1) = 1, [isList](x0) = 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = 1 orientation: active#(U41(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U42(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U43(X)) = X + 2 >= X + 1 = active#(X) active#(U51(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U53(X)) = X + 2 >= X + 1 = active#(X) active#(U61(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(U62(X)) = X + 2 >= X + 1 = active#(X) active#(U71(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(and(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = 1 >= 1 = __(active(X1),X2) active(__(X1,X2)) = 1 >= 1 = __(X1,active(X2)) active(U11(X1,X2)) = 1 >= 1 = U11(active(X1),X2) active(U12(X)) = 1 >= 1 = U12(active(X)) active(U21(X1,X2,X3)) = 1 >= 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = 1 >= 1 = U22(active(X1),X2) active(U23(X)) = 1 >= 1 = U23(active(X)) active(U31(X1,X2)) = 1 >= 1 = U31(active(X1),X2) active(U32(X)) = 1 >= 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = 1 >= 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = 1 >= 1 = U72(active(X)) active(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(active(X1),X2) __(mark(X1),X2) = 1 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 1 = mark(__(X1,X2)) U11(mark(X1),X2) = 1 >= 1 = mark(U11(X1,X2)) U12(mark(X)) = 1 >= 1 = mark(U12(X)) U21(mark(X1),X2,X3) = 1 >= 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = 1 >= 1 = mark(U22(X1,X2)) U23(mark(X)) = 1 >= 1 = mark(U23(X)) U31(mark(X1),X2) = 1 >= 1 = mark(U31(X1,X2)) U32(mark(X)) = 1 >= 1 = mark(U32(X)) U41(mark(X1),X2,X3) = 2 >= 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = 2 >= 1 = mark(U42(X1,X2)) U43(mark(X)) = 2 >= 1 = mark(U43(X)) U51(mark(X1),X2,X3) = 2 >= 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = 1 >= 1 = mark(U52(X1,X2)) U53(mark(X)) = 2 >= 1 = mark(U53(X)) U61(mark(X1),X2) = 2 >= 1 = mark(U61(X1,X2)) U62(mark(X)) = 2 >= 1 = mark(U62(X)) U71(mark(X1),X2) = 2 >= 1 = mark(U71(X1,X2)) U72(mark(X)) = 1 >= 1 = mark(U72(X)) and(mark(X1),X2) = 2 >= 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 1 >= 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 1 >= 1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 1 >= 1 = U12(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 1 >= 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 1 >= 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 1 >= 1 = isList(proper(X)) proper(U23(X)) = 1 >= 1 = U23(proper(X)) proper(U31(X1,X2)) = 1 >= 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = 1 >= 1 = U32(proper(X)) proper(isQid(X)) = 1 >= 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 1 >= 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = 1 >= 1 = U72(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 1 >= 1 = isPalListKind(proper(X)) proper(isPal(X)) = 1 >= 1 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 1 >= 1 = ok(U11(X1,X2)) U12(ok(X)) = 1 >= 1 = ok(U12(X)) isNeList(ok(X)) = 1 >= 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = 1 >= 1 = ok(U22(X1,X2)) isList(ok(X)) = 1 >= 1 = ok(isList(X)) U23(ok(X)) = 1 >= 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = 1 >= 1 = ok(U31(X1,X2)) U32(ok(X)) = 1 >= 1 = ok(U32(X)) isQid(ok(X)) = 1 >= 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = 1 >= 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U71(X1,X2)) U72(ok(X)) = 1 >= 1 = ok(U72(X)) isNePal(ok(X)) = 1 >= 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = 1 >= 1 = ok(isPalListKind(X)) isPal(ok(X)) = 1 >= 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(U11(X1,X2)) -> proper#(X2) proper#(U11(X1,X2)) -> proper#(X1) proper#(U12(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2)) -> proper#(X2) proper#(U22(X1,X2)) -> proper#(X1) proper#(isList(X)) -> proper#(X) proper#(U23(X)) -> proper#(X) proper#(U31(X1,X2)) -> proper#(X2) proper#(U31(X1,X2)) -> proper#(X1) proper#(U32(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) proper#(U41(X1,X2,X3)) -> proper#(X3) proper#(U41(X1,X2,X3)) -> proper#(X2) proper#(U41(X1,X2,X3)) -> proper#(X1) proper#(U42(X1,X2)) -> proper#(X2) proper#(U42(X1,X2)) -> proper#(X1) proper#(U43(X)) -> proper#(X) proper#(U51(X1,X2,X3)) -> proper#(X3) proper#(U51(X1,X2,X3)) -> proper#(X2) proper#(U51(X1,X2,X3)) -> proper#(X1) proper#(U52(X1,X2)) -> proper#(X2) proper#(U52(X1,X2)) -> proper#(X1) proper#(U53(X)) -> proper#(X) proper#(U61(X1,X2)) -> proper#(X2) proper#(U61(X1,X2)) -> proper#(X1) proper#(U62(X)) -> proper#(X) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U72(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) proper#(and(X1,X2)) -> proper#(X2) proper#(and(X1,X2)) -> proper#(X1) proper#(isPalListKind(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0 + x1 + 1, [U72](x0) = x0 + 1, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x0 + x1 + 1, [U62](x0) = x0 + 1, [U61](x0, x1) = x0 + x1 + 1, [U53](x0) = x0 + 1, [U52](x0, x1) = x0 + x1 + 1, [U51](x0, x1, x2) = x0 + x1 + x2 + 1, [U43](x0) = x0 + 1, [U42](x0, x1) = x0 + x1 + 1, [U41](x0, x1, x2) = x0 + x1 + x2 + 1, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0 + x1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0 + x1 + x2 + 1, [U12](x0) = x0 + 1, [isNeList](x0) = x0 + 1, [U11](x0, x1) = x0 + x1 + 1, [tt] = 1, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: proper#(__(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(__(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U11(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U11(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U12(X)) = X + 2 >= X + 1 = proper#(X) proper#(isNeList(X)) = X + 2 >= X + 1 = proper#(X) proper#(U21(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U21(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U21(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U22(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = proper#(X2) proper#(U22(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = proper#(X1) proper#(isList(X)) = X + 1 >= X + 1 = proper#(X) proper#(U23(X)) = X + 1 >= X + 1 = proper#(X) proper#(U31(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = proper#(X2) proper#(U31(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = proper#(X1) proper#(U32(X)) = X + 1 >= X + 1 = proper#(X) proper#(isQid(X)) = X + 1 >= X + 1 = proper#(X) proper#(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U42(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U42(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U43(X)) = X + 2 >= X + 1 = proper#(X) proper#(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(U51(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(U52(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U52(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U53(X)) = X + 2 >= X + 1 = proper#(X) proper#(U61(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U61(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U62(X)) = X + 2 >= X + 1 = proper#(X) proper#(U71(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U71(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U72(X)) = X + 2 >= X + 1 = proper#(X) proper#(isNePal(X)) = X + 2 >= X + 1 = proper#(X) proper#(and(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(and(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(isPalListKind(X)) = X + 1 >= X + 1 = proper#(X) proper#(isPal(X)) = X + 1 >= X + 1 = proper#(X) active(__(__(X,Y),Z)) = X + Y + Z + 2 >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 2 >= 0 = mark(X) active(__(nil(),X)) = X + 2 >= 0 = mark(X) active(U11(tt(),V)) = V + 2 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 2 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 + V2 + 2 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V1 + V2 + 2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 + 2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 2 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V1 + V2 + 2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 2 >= 0 = mark(tt()) active(U61(tt(),V)) = V + 2 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 2 >= 0 = mark(tt()) active(U71(tt(),V)) = V + 2 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 2 >= 0 = mark(tt()) active(and(tt(),X)) = X + 2 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V + 1 >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 + V2 + 2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 2I + P + 3 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 + V2 + 1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + X2 >= X1 + X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X2 + 1 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + 1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 + 1 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 1 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = X2 + X3 + 1 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X2 + X3 + 1 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 + 1 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 1 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X2 + X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 1 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 + 1 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 1 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 + 1 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 1 >= 0 = mark(U72(X)) and(mark(X1),X2) = X2 + 1 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 + X2 >= X1 + X2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 + X2 >= X1 + X2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X >= X = isPalListKind(proper(X)) proper(isPal(X)) = X >= X = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U22(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X >= X = ok(isPalListKind(X)) isPal(ok(X)) = X >= X = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: proper#(U22(X1,X2)) -> proper#(X2) proper#(U22(X1,X2)) -> proper#(X1) proper#(isList(X)) -> proper#(X) proper#(U23(X)) -> proper#(X) proper#(U31(X1,X2)) -> proper#(X2) proper#(U31(X1,X2)) -> proper#(X1) proper#(U32(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) proper#(isPalListKind(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0 + 1, [and](x0, x1) = 1, [U72](x0) = 1, [isNePal](x0) = 1, [U71](x0, x1) = 1, [U62](x0) = 1, [U61](x0, x1) = 1, [U53](x0) = 1, [U52](x0, x1) = 1, [U51](x0, x1, x2) = 1, [U43](x0) = 1, [U42](x0, x1) = 1, [U41](x0, x1, x2) = 1, [U32](x0) = x0 + 1, [isQid](x0) = x0 + 1, [U31](x0, x1) = x0 + x1 + 1, [U23](x0) = x0 + 1, [U22](x0, x1) = x0 + x1 + 1, [isList](x0) = x0 + 1, [U21](x0, x1, x2) = 1, [U12](x0) = 1, [isNeList](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [nil] = 0, [mark](x0) = 1, [active](x0) = x0, [__](x0, x1) = 1 orientation: proper#(U22(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U22(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(isList(X)) = X + 2 >= X + 1 = proper#(X) proper#(U23(X)) = X + 2 >= X + 1 = proper#(X) proper#(U31(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(U31(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(U32(X)) = X + 2 >= X + 1 = proper#(X) proper#(isQid(X)) = X + 2 >= X + 1 = proper#(X) proper#(isPalListKind(X)) = X + 2 >= X + 1 = proper#(X) proper#(isPal(X)) = X + 2 >= X + 1 = proper#(X) active(__(__(X,Y),Z)) = 1 >= 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 1 = mark(X) active(__(nil(),X)) = 1 >= 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = 1 >= 1 = mark(X) active(isList(V)) = V + 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 2 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 2 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = 1 >= 1 = __(active(X1),X2) active(__(X1,X2)) = 1 >= 1 = __(X1,active(X2)) active(U11(X1,X2)) = 1 >= 1 = U11(active(X1),X2) active(U12(X)) = 1 >= 1 = U12(active(X)) active(U21(X1,X2,X3)) = 1 >= 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = 1 >= 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = 1 >= 1 = U42(active(X1),X2) active(U43(X)) = 1 >= 1 = U43(active(X)) active(U51(X1,X2,X3)) = 1 >= 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = 1 >= 1 = U52(active(X1),X2) active(U53(X)) = 1 >= 1 = U53(active(X)) active(U61(X1,X2)) = 1 >= 1 = U61(active(X1),X2) active(U62(X)) = 1 >= 1 = U62(active(X)) active(U71(X1,X2)) = 1 >= 1 = U71(active(X1),X2) active(U72(X)) = 1 >= 1 = U72(active(X)) active(and(X1,X2)) = 1 >= 1 = and(active(X1),X2) __(mark(X1),X2) = 1 >= 1 = mark(__(X1,X2)) __(X1,mark(X2)) = 1 >= 1 = mark(__(X1,X2)) U11(mark(X1),X2) = 1 >= 1 = mark(U11(X1,X2)) U12(mark(X)) = 1 >= 1 = mark(U12(X)) U21(mark(X1),X2,X3) = 1 >= 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 2 >= 1 = mark(U22(X1,X2)) U23(mark(X)) = 2 >= 1 = mark(U23(X)) U31(mark(X1),X2) = X2 + 2 >= 1 = mark(U31(X1,X2)) U32(mark(X)) = 2 >= 1 = mark(U32(X)) U41(mark(X1),X2,X3) = 1 >= 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = 1 >= 1 = mark(U42(X1,X2)) U43(mark(X)) = 1 >= 1 = mark(U43(X)) U51(mark(X1),X2,X3) = 1 >= 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = 1 >= 1 = mark(U52(X1,X2)) U53(mark(X)) = 1 >= 1 = mark(U53(X)) U61(mark(X1),X2) = 1 >= 1 = mark(U61(X1,X2)) U62(mark(X)) = 1 >= 1 = mark(U62(X)) U71(mark(X1),X2) = 1 >= 1 = mark(U71(X1,X2)) U72(mark(X)) = 1 >= 1 = mark(U72(X)) and(mark(X1),X2) = 1 >= 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 1 >= 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 1 >= 1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 1 >= 1 = U12(proper(X)) proper(isNeList(X)) = 1 >= 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 1 >= 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 1 >= 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 1 >= 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = 1 >= 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = 1 >= 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 1 >= 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = 1 >= 1 = U53(proper(X)) proper(U61(X1,X2)) = 1 >= 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = 1 >= 1 = U62(proper(X)) proper(U71(X1,X2)) = 1 >= 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = 1 >= 1 = U72(proper(X)) proper(isNePal(X)) = 1 >= 1 = isNePal(proper(X)) proper(and(X1,X2)) = 1 >= 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 1 >= 0 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = 1 >= 0 = ok(U11(X1,X2)) U12(ok(X)) = 1 >= 0 = ok(U12(X)) isNeList(ok(X)) = 1 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = 1 >= 0 = ok(U22(X1,X2)) isList(ok(X)) = 1 >= 0 = ok(isList(X)) U23(ok(X)) = 1 >= 0 = ok(U23(X)) U31(ok(X1),ok(X2)) = 1 >= 0 = ok(U31(X1,X2)) U32(ok(X)) = 1 >= 0 = ok(U32(X)) isQid(ok(X)) = 1 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = 1 >= 0 = ok(U42(X1,X2)) U43(ok(X)) = 1 >= 0 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = 1 >= 0 = ok(U52(X1,X2)) U53(ok(X)) = 1 >= 0 = ok(U53(X)) U61(ok(X1),ok(X2)) = 1 >= 0 = ok(U61(X1,X2)) U62(ok(X)) = 1 >= 0 = ok(U62(X)) U71(ok(X1),ok(X2)) = 1 >= 0 = ok(U71(X1,X2)) U72(ok(X)) = 1 >= 0 = ok(U72(X)) isNePal(ok(X)) = 1 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = 1 >= 0 = ok(and(X1,X2)) isPalListKind(ok(X)) = 1 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 1 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isPal#(ok(X)) -> isPal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isPal#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: isPal#(ok(X)) = X + 2 >= X + 1 = isPal#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isPalListKind#(ok(X)) -> isPalListKind#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isPalListKind#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: isPalListKind#(ok(X)) = X + 2 >= X + 1 = isPalListKind#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(ok(X1),ok(X2)) -> and#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [and#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: and#(mark(X1),X2) = X2 + 1 >= X2 + 1 = and#(X1,X2) and#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = and#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: and#(mark(X1),X2) -> and#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [and#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: and#(mark(X1),X2) = X1 + 1 >= X1 = and#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNePal#(ok(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isNePal#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: isNePal#(ok(X)) = X + 2 >= X + 1 = isNePal#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U72#(mark(X)) -> U72#(X) U72#(ok(X)) -> U72#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U72#](x0) = x0, [top](x0) = 1, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U72#(mark(X)) = X + 1 >= X = U72#(X) U72#(ok(X)) = X >= X = U72#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: U72#(ok(X)) -> U72#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U72#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U72#(ok(X)) = X + 2 >= X + 1 = U72#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U71#(mark(X1),X2) -> U71#(X1,X2) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U71#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U71#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U71#(X1,X2) U71#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U71#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U71#(mark(X1),X2) -> U71#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U71#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U71#(mark(X1),X2) = X1 + 1 >= X1 = U71#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U62#(mark(X)) -> U62#(X) U62#(ok(X)) -> U62#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U62#](x0) = x0, [top](x0) = 1, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U62#(mark(X)) = X + 1 >= X = U62#(X) U62#(ok(X)) = X >= X = U62#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: U62#(ok(X)) -> U62#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U62#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U62#(ok(X)) = X + 2 >= X + 1 = U62#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U61#(mark(X1),X2) -> U61#(X1,X2) U61#(ok(X1),ok(X2)) -> U61#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U61#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U61#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U61#(X1,X2) U61#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U61#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U61#(mark(X1),X2) -> U61#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U61#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U61#(mark(X1),X2) = X1 + 1 >= X1 = U61#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U53#(mark(X)) -> U53#(X) U53#(ok(X)) -> U53#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U53#](x0) = x0, [top](x0) = 1, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U53#(mark(X)) = X + 1 >= X = U53#(X) U53#(ok(X)) = X >= X = U53#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: U53#(ok(X)) -> U53#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U53#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U53#(ok(X)) = X + 2 >= X + 1 = U53#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U52#(mark(X1),X2) -> U52#(X1,X2) U52#(ok(X1),ok(X2)) -> U52#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U52#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U52#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U52#(X1,X2) U52#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U52#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U52#(mark(X1),X2) -> U52#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U52#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U52#(mark(X1),X2) = X1 + 1 >= X1 = U52#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3) U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U51#](x0, x1, x2) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U51#(mark(X1),X2,X3) = X1 + 1 >= X1 = U51#(X1,X2,X3) U51#(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = U51#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U51#](x0, x1, x2) = x1 + x2, [top](x0) = 1, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = x0, [isPalListKind](x0) = x0 + 1, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0 + 1, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0 + 1, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U51#(ok(X1),ok(X2),ok(X3)) = X2 + X3 + 2 >= X2 + X3 = U51#(X1,X2,X3) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 2 >= 0 = mark(tt()) active(isPalListKind(e())) = 2 >= 0 = mark(tt()) active(isPalListKind(i())) = 2 >= 0 = mark(tt()) active(isPalListKind(nil())) = 2 >= 0 = mark(tt()) active(isPalListKind(o())) = 2 >= 0 = mark(tt()) active(isPalListKind(u())) = 2 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 >= X1 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X1 >= X1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X1 >= X1 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 1 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = 0 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = 0 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = 0 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 + 2 >= X1 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 2 >= X + 2 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 2 >= 2 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 2 >= X + 2 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U43#(mark(X)) -> U43#(X) U43#(ok(X)) -> U43#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U43#](x0) = x0, [top](x0) = 1, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U43#(mark(X)) = X + 1 >= X = U43#(X) U43#(ok(X)) = X >= X = U43#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: U43#(ok(X)) -> U43#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U43#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U43#(ok(X)) = X + 2 >= X + 1 = U43#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U42#(mark(X1),X2) -> U42#(X1,X2) U42#(ok(X1),ok(X2)) -> U42#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U42#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U42#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U42#(X1,X2) U42#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U42#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U42#(mark(X1),X2) -> U42#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U42#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U42#(mark(X1),X2) = X1 + 1 >= X1 = U42#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U41#](x0, x1, x2) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U41#(mark(X1),X2,X3) = X1 + 1 >= X1 = U41#(X1,X2,X3) U41#(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = U41#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U41#](x0, x1, x2) = x1 + x2, [top](x0) = 1, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = x0, [isPalListKind](x0) = x0 + 1, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0 + 1, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0 + 1, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U41#(ok(X1),ok(X2),ok(X3)) = X2 + X3 + 2 >= X2 + X3 = U41#(X1,X2,X3) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 2 >= 0 = mark(tt()) active(isPalListKind(e())) = 2 >= 0 = mark(tt()) active(isPalListKind(i())) = 2 >= 0 = mark(tt()) active(isPalListKind(nil())) = 2 >= 0 = mark(tt()) active(isPalListKind(o())) = 2 >= 0 = mark(tt()) active(isPalListKind(u())) = 2 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 >= X1 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X1 >= X1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X1 >= X1 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 1 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = 0 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = 0 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = 0 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 + 2 >= X1 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 2 >= X + 2 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 2 >= 2 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 2 >= X + 2 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isQid#(ok(X)) -> isQid#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isQid#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: isQid#(ok(X)) = X + 2 >= X + 1 = isQid#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U32#(mark(X)) -> U32#(X) U32#(ok(X)) -> U32#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U32#](x0) = x0, [top](x0) = 1, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U32#(mark(X)) = X + 1 >= X = U32#(X) U32#(ok(X)) = X >= X = U32#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: U32#(ok(X)) -> U32#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U32#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U32#(ok(X)) = X + 2 >= X + 1 = U32#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U31#(mark(X1),X2) -> U31#(X1,X2) U31#(ok(X1),ok(X2)) -> U31#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U31#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U31#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U31#(X1,X2) U31#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U31#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U31#(mark(X1),X2) -> U31#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U31#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U31#(mark(X1),X2) = X1 + 1 >= X1 = U31#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U23#(mark(X)) -> U23#(X) U23#(ok(X)) -> U23#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U23#](x0) = x0, [top](x0) = 1, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U23#(mark(X)) = X + 1 >= X = U23#(X) U23#(ok(X)) = X >= X = U23#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: U23#(ok(X)) -> U23#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U23#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U23#(ok(X)) = X + 2 >= X + 1 = U23#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isList#(ok(X)) -> isList#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isList#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: isList#(ok(X)) = X + 2 >= X + 1 = isList#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U22#(mark(X1),X2) -> U22#(X1,X2) U22#(ok(X1),ok(X2)) -> U22#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U22#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U22#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U22#(X1,X2) U22#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U22#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U22#(mark(X1),X2) -> U22#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U22#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U22#(mark(X1),X2) = X1 + 1 >= X1 = U22#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U21#](x0, x1, x2) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U21#(mark(X1),X2,X3) = X1 + 1 >= X1 = U21#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = U21#(X1,X2,X3) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U21#](x0, x1, x2) = x1 + x2, [top](x0) = 1, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 1, [o] = 1, [i] = 1, [e] = 1, [a] = 1, [isPal](x0) = x0, [isPalListKind](x0) = x0 + 1, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0 + 1, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0 + 1, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x2, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 1, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U21#(ok(X1),ok(X2),ok(X3)) = X2 + X3 + 2 >= X2 + X3 = U21#(X1,X2,X3) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 1 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V2 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 0 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = 0 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = 0 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 2 >= 0 = mark(tt()) active(isPalListKind(e())) = 2 >= 0 = mark(tt()) active(isPalListKind(i())) = 2 >= 0 = mark(tt()) active(isPalListKind(nil())) = 2 >= 0 = mark(tt()) active(isPalListKind(o())) = 2 >= 0 = mark(tt()) active(isPalListKind(u())) = 2 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 + 1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 1 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X3 >= X3 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X1 >= X1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 >= X1 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X1 >= X1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X1 >= X1 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = X3 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = 0 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 1 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = 0 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = 0 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = 0 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 2 >= X1 + 2 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 + 2 >= X1 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 2 >= X + 2 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 2 >= 2 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 2 >= X1 + 2 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 2 >= X + 2 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNeList#(ok(X)) -> isNeList#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [isNeList#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: isNeList#(ok(X)) = X + 2 >= X + 1 = isNeList#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U12#(mark(X)) -> U12#(X) U12#(ok(X)) -> U12#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U12#](x0) = x0, [top](x0) = 1, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: U12#(mark(X)) = X + 1 >= X = U12#(X) U12#(ok(X)) = X >= X = U12#(X) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 1 >= 1 = top(proper(X)) top(ok(X)) = 1 >= 1 = top(active(X)) problem: DPs: U12#(ok(X)) -> U12#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U12#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x1 orientation: U12#(ok(X)) = X + 2 >= X + 1 = U12#(X) active(__(__(X,Y),Z)) = Z >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 0 >= 0 = mark(X) active(__(nil(),X)) = X >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V + 1 >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = V >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V2 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V2 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V2 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X2 >= X2 = __(active(X1),X2) active(__(X1,X2)) = X2 >= X2 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 >= X2 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X1 >= X1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X2 >= X2 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = X2 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = 0 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 + 1 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = 0 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = X2 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X2 + 1 >= X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 2 >= X2 + 2 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X2 + 1 >= X2 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U11#(mark(X1),X2) -> U11#(X1,X2) U11#(ok(X1),ok(X2)) -> U11#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U11#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 0, [o] = 1, [i] = 1, [e] = 0, [a] = 1, [isPal](x0) = x0 + 1, [isPalListKind](x0) = x0, [and](x0, x1) = x0, [U72](x0) = x0, [isNePal](x0) = x0 + 1, [U71](x0, x1) = x1, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x1 + 1, [U51](x0, x1, x2) = x2 + 1, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x1 + 1, [isList](x0) = x0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: U11#(mark(X1),X2) = X2 + 1 >= X2 + 1 = U11#(X1,X2) U11#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = U11#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = 0 >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = 0 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = V2 + 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 + 1 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 + 1 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),V)) = 0 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),V)) = V >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(and(tt(),X)) = 0 >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V + 1 >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I + 1 >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V + 1 >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 0 = mark(tt()) active(isPalListKind(a())) = 1 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 1 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 1 >= 0 = mark(tt()) active(isPalListKind(u())) = 0 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 1 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 >= X1 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X1 >= X1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X2 + 1 >= X2 + 1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 >= X1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X2 >= X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X1 >= X1 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = 0 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = 0 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X2 + 1 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 + 1 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 + 1 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 0 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = X2 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = 0 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X2 + 2 >= X2 + 2 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 2 >= X3 + 2 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 2 >= X2 + 2 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X2 + 1 >= X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + 1 >= X1 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 2 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: U11#(mark(X1),X2) -> U11#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [U11#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: U11#(mark(X1),X2) = X1 + 1 >= X1 = U11#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x0, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = 0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 orientation: __#(mark(X1),X2) = X1 + 1 >= X1 = __#(X1,X2) __#(X1,mark(X2)) = X1 >= X1 = __#(X1,X2) __#(ok(X1),ok(X2)) = X1 >= X1 = __#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 1 >= X + 1 = mark(X) active(__(nil(),X)) = X + 1 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = 0 >= 0 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X1,X2)) = 0 >= 0 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 0 >= 0 = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = 0 >= 0 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = 0 >= 0 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = 0 >= 0 = U23(proper(X)) proper(U31(X1,X2)) = 0 >= 0 = U31(proper(X1),proper(X2)) proper(U32(X)) = 0 >= 0 = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = 0 >= 0 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = 0 >= 0 = U42(proper(X1),proper(X2)) proper(U43(X)) = 0 >= 0 = U43(proper(X)) proper(U51(X1,X2,X3)) = 0 >= 0 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = 0 >= 0 = U52(proper(X1),proper(X2)) proper(U53(X)) = 0 >= 0 = U53(proper(X)) proper(U61(X1,X2)) = 0 >= 0 = U61(proper(X1),proper(X2)) proper(U62(X)) = 0 >= 0 = U62(proper(X)) proper(U71(X1,X2)) = 0 >= 0 = U71(proper(X1),proper(X2)) proper(U72(X)) = 0 >= 0 = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = 0 >= 0 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 1, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = x0, [isPalListKind](x0) = x0, [and](x0, x1) = x1, [U72](x0) = x0, [isNePal](x0) = x0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0 + 1, [U53](x0) = x0, [U52](x0, x1) = x1, [U51](x0, x1, x2) = x2, [U43](x0) = x0, [U42](x0, x1) = x1, [U41](x0, x1, x2) = x2, [U32](x0) = x0, [isQid](x0) = x0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = x0, [U21](x0, x1, x2) = x1, [U12](x0) = x0, [isNeList](x0) = x0, [U11](x0, x1) = x1, [tt] = 1, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = x0 orientation: __#(X1,mark(X2)) = X1 + 1 >= X1 + 1 = __#(X1,X2) __#(ok(X1),ok(X2)) = X1 + 2 >= X1 + 1 = __#(X1,X2) active(__(__(X,Y),Z)) = X >= 0 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= 0 = mark(X) active(__(nil(),X)) = 0 >= 0 = mark(X) active(U11(tt(),V)) = V >= 0 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 0 = mark(tt()) active(U21(tt(),V1,V2)) = V1 >= 0 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 0 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 0 = mark(tt()) active(U31(tt(),V)) = V >= 0 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= 0 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = V2 >= 0 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 0 = mark(tt()) active(U51(tt(),V1,V2)) = V2 >= 0 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = V2 >= 0 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 0 = mark(tt()) active(U61(tt(),V)) = 2 >= 0 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 0 = mark(tt()) active(U71(tt(),V)) = 1 >= 0 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 0 = mark(tt()) active(and(tt(),X)) = X >= 0 = mark(X) active(isList(V)) = V >= 0 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 >= 0 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = V >= 0 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = V1 >= 0 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = V >= 0 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = I >= 0 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = V >= 0 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(a())) = 0 >= 0 = mark(tt()) active(isPalListKind(e())) = 0 >= 0 = mark(tt()) active(isPalListKind(i())) = 0 >= 0 = mark(tt()) active(isPalListKind(nil())) = 0 >= 0 = mark(tt()) active(isPalListKind(o())) = 0 >= 0 = mark(tt()) active(isPalListKind(u())) = 1 >= 0 = mark(tt()) active(isPalListKind(__(V1,V2))) = V1 >= 0 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 1 >= 0 = mark(tt()) active(__(X1,X2)) = X1 >= X1 = __(active(X1),X2) active(__(X1,X2)) = X1 >= X1 = __(X1,active(X2)) active(U11(X1,X2)) = X2 >= X2 = U11(active(X1),X2) active(U12(X)) = X >= X = U12(active(X)) active(U21(X1,X2,X3)) = X2 >= X2 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 >= X1 = U22(active(X1),X2) active(U23(X)) = X >= X = U23(active(X)) active(U31(X1,X2)) = X2 >= X2 = U31(active(X1),X2) active(U32(X)) = X >= X = U32(active(X)) active(U41(X1,X2,X3)) = X3 >= X3 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X2 >= X2 = U42(active(X1),X2) active(U43(X)) = X >= X = U43(active(X)) active(U51(X1,X2,X3)) = X3 >= X3 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X2 >= X2 = U52(active(X1),X2) active(U53(X)) = X >= X = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X >= X = U62(active(X)) active(U71(X1,X2)) = X1 >= X1 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(and(X1,X2)) = X2 >= X2 = and(active(X1),X2) __(mark(X1),X2) = 0 >= 0 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 >= 0 = mark(__(X1,X2)) U11(mark(X1),X2) = X2 >= 0 = mark(U11(X1,X2)) U12(mark(X)) = 0 >= 0 = mark(U12(X)) U21(mark(X1),X2,X3) = X2 >= 0 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = 0 >= 0 = mark(U22(X1,X2)) U23(mark(X)) = 0 >= 0 = mark(U23(X)) U31(mark(X1),X2) = X2 >= 0 = mark(U31(X1,X2)) U32(mark(X)) = 0 >= 0 = mark(U32(X)) U41(mark(X1),X2,X3) = X3 >= 0 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X2 >= 0 = mark(U42(X1,X2)) U43(mark(X)) = 0 >= 0 = mark(U43(X)) U51(mark(X1),X2,X3) = X3 >= 0 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X2 >= 0 = mark(U52(X1,X2)) U53(mark(X)) = 0 >= 0 = mark(U53(X)) U61(mark(X1),X2) = 1 >= 0 = mark(U61(X1,X2)) U62(mark(X)) = 0 >= 0 = mark(U62(X)) U71(mark(X1),X2) = 0 >= 0 = mark(U71(X1,X2)) U72(mark(X)) = 0 >= 0 = mark(U72(X)) and(mark(X1),X2) = X2 >= 0 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + 1 >= X1 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X2 + 1 >= X2 + 1 = U11(proper(X1),proper(X2)) proper(tt()) = 2 >= 2 = ok(tt()) proper(U12(X)) = X + 1 >= X + 1 = U12(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X2 + 1 >= X2 + 1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(proper(X1),proper(X2)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U23(X)) = X + 1 >= X + 1 = U23(proper(X)) proper(U31(X1,X2)) = X2 + 1 >= X2 + 1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X + 1 >= X + 1 = U32(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X2 + 1 >= X2 + 1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X + 1 >= X + 1 = U43(proper(X)) proper(U51(X1,X2,X3)) = X3 + 1 >= X3 + 1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X2 + 1 >= X2 + 1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X + 1 >= X + 1 = U53(proper(X)) proper(U61(X1,X2)) = X1 + 2 >= X1 + 2 = U61(proper(X1),proper(X2)) proper(U62(X)) = X + 1 >= X + 1 = U62(proper(X)) proper(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 1 >= X + 1 = U72(proper(X)) proper(isNePal(X)) = X + 1 >= X + 1 = isNePal(proper(X)) proper(and(X1,X2)) = X2 + 1 >= X2 + 1 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = X + 1 >= X + 1 = isPalListKind(proper(X)) proper(isPal(X)) = X + 1 >= X + 1 = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 2 >= 2 = ok(u()) __(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U11(X1,X2)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U22(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U23(ok(X)) = X + 1 >= X + 1 = ok(U23(X)) U31(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U31(X1,X2)) U32(ok(X)) = X + 1 >= X + 1 = ok(U32(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U42(X1,X2)) U43(ok(X)) = X + 1 >= X + 1 = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(U52(X1,X2)) U53(ok(X)) = X + 1 >= X + 1 = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(U61(X1,X2)) U62(ok(X)) = X + 1 >= X + 1 = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 1 >= X + 1 = ok(U72(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(and(X1,X2)) isPalListKind(ok(X)) = X + 1 >= X + 1 = ok(isPalListKind(X)) isPal(ok(X)) = X + 1 >= X + 1 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: __#(X1,mark(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [__#](x0, x1) = x1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 0, [isPalListKind](x0) = 0, [and](x0, x1) = x0 + x1, [U72](x0) = x0, [isNePal](x0) = 0, [U71](x0, x1) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U53](x0) = x0, [U52](x0, x1) = x0, [U51](x0, x1, x2) = x0, [U43](x0) = x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = x0, [U32](x0) = x0, [isQid](x0) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [isList](x0) = 0, [U21](x0, x1, x2) = x0, [U12](x0) = x0, [isNeList](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [__](x0, x1) = x0 + x1 + 1 orientation: __#(X1,mark(X2)) = X2 + 1 >= X2 = __#(X1,X2) active(__(__(X,Y),Z)) = X + Y + Z + 3 >= X + Y + Z + 3 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 3 >= X + 1 = mark(X) active(__(nil(),X)) = X + 3 >= X + 1 = mark(X) active(U11(tt(),V)) = 1 >= 1 = mark(U12(isNeList(V))) active(U12(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1,V2)) = 1 >= 1 = mark(U22(isList(V1),V2)) active(U22(tt(),V2)) = 1 >= 1 = mark(U23(isList(V2))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isQid(V))) active(U32(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isList(V1),V2)) active(U42(tt(),V2)) = 1 >= 1 = mark(U43(isNeList(V2))) active(U43(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V1,V2)) = 1 >= 1 = mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) = 1 >= 1 = mark(U53(isList(V2))) active(U53(tt())) = 1 >= 1 = mark(tt()) active(U61(tt(),V)) = 1 >= 1 = mark(U62(isQid(V))) active(U62(tt())) = 1 >= 1 = mark(tt()) active(U71(tt(),V)) = 1 >= 1 = mark(U72(isNePal(V))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(and(tt(),X)) = X + 1 >= X + 1 = mark(X) active(isList(V)) = 1 >= 1 = mark(U11(isPalListKind(V),V)) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 1 >= 1 = mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) = 1 >= 1 = mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) = 1 >= 1 = mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) = 1 >= 1 = mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) = 1 >= 1 = mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) = 1 >= 1 = mark(U71(isPalListKind(V),V)) active(isPal(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(a())) = 1 >= 1 = mark(tt()) active(isPalListKind(e())) = 1 >= 1 = mark(tt()) active(isPalListKind(i())) = 1 >= 1 = mark(tt()) active(isPalListKind(nil())) = 1 >= 1 = mark(tt()) active(isPalListKind(o())) = 1 >= 1 = mark(tt()) active(isPalListKind(u())) = 1 >= 1 = mark(tt()) active(isPalListKind(__(V1,V2))) = 1 >= 1 = mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,active(X2)) active(U11(X1,X2)) = X1 + 1 >= X1 + 1 = U11(active(X1),X2) active(U12(X)) = X + 1 >= X + 1 = U12(active(X)) active(U21(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U21(active(X1),X2,X3) active(U22(X1,X2)) = X1 + 1 >= X1 + 1 = U22(active(X1),X2) active(U23(X)) = X + 1 >= X + 1 = U23(active(X)) active(U31(X1,X2)) = X1 + 1 >= X1 + 1 = U31(active(X1),X2) active(U32(X)) = X + 1 >= X + 1 = U32(active(X)) active(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U41(active(X1),X2,X3) active(U42(X1,X2)) = X1 + 1 >= X1 + 1 = U42(active(X1),X2) active(U43(X)) = X + 1 >= X + 1 = U43(active(X)) active(U51(X1,X2,X3)) = X1 + 1 >= X1 + 1 = U51(active(X1),X2,X3) active(U52(X1,X2)) = X1 + 1 >= X1 + 1 = U52(active(X1),X2) active(U53(X)) = X + 1 >= X + 1 = U53(active(X)) active(U61(X1,X2)) = X1 + 1 >= X1 + 1 = U61(active(X1),X2) active(U62(X)) = X + 1 >= X + 1 = U62(active(X)) active(U71(X1,X2)) = X1 + 1 >= X1 + 1 = U71(active(X1),X2) active(U72(X)) = X + 1 >= X + 1 = U72(active(X)) active(and(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U11(X1,X2)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) U21(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U21(X1,X2,X3)) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U22(X1,X2)) U23(mark(X)) = X + 1 >= X + 1 = mark(U23(X)) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U31(X1,X2)) U32(mark(X)) = X + 1 >= X + 1 = mark(U32(X)) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U41(X1,X2,X3)) U42(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U42(X1,X2)) U43(mark(X)) = X + 1 >= X + 1 = mark(U43(X)) U51(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = mark(U51(X1,X2,X3)) U52(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U52(X1,X2)) U53(mark(X)) = X + 1 >= X + 1 = mark(U53(X)) U61(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U61(X1,X2)) U62(mark(X)) = X + 1 >= X + 1 = mark(U62(X)) U71(mark(X1),X2) = X1 + 1 >= X1 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 1 >= X + 1 = mark(U72(X)) and(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X1,X2)) = X1 >= X1 = U11(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNeList(X)) = 0 >= 0 = isNeList(proper(X)) proper(U21(X1,X2,X3)) = X1 >= X1 = U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) = X1 >= X1 = U22(proper(X1),proper(X2)) proper(isList(X)) = 0 >= 0 = isList(proper(X)) proper(U23(X)) = X >= X = U23(proper(X)) proper(U31(X1,X2)) = X1 >= X1 = U31(proper(X1),proper(X2)) proper(U32(X)) = X >= X = U32(proper(X)) proper(isQid(X)) = 0 >= 0 = isQid(proper(X)) proper(U41(X1,X2,X3)) = X1 >= X1 = U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) = X1 >= X1 = U42(proper(X1),proper(X2)) proper(U43(X)) = X >= X = U43(proper(X)) proper(U51(X1,X2,X3)) = X1 >= X1 = U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) = X1 >= X1 = U52(proper(X1),proper(X2)) proper(U53(X)) = X >= X = U53(proper(X)) proper(U61(X1,X2)) = X1 >= X1 = U61(proper(X1),proper(X2)) proper(U62(X)) = X >= X = U62(proper(X)) proper(U71(X1,X2)) = X1 >= X1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isNePal(X)) = 0 >= 0 = isNePal(proper(X)) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(isPalListKind(X)) = 0 >= 0 = isPalListKind(proper(X)) proper(isPal(X)) = 0 >= 0 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X1),ok(X2)) = X1 >= X1 = ok(U11(X1,X2)) U12(ok(X)) = X >= X = ok(U12(X)) isNeList(ok(X)) = 0 >= 0 = ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) = X1 >= X1 = ok(U22(X1,X2)) isList(ok(X)) = 0 >= 0 = ok(isList(X)) U23(ok(X)) = X >= X = ok(U23(X)) U31(ok(X1),ok(X2)) = X1 >= X1 = ok(U31(X1,X2)) U32(ok(X)) = X >= X = ok(U32(X)) isQid(ok(X)) = 0 >= 0 = ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) = X1 >= X1 = ok(U42(X1,X2)) U43(ok(X)) = X >= X = ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) = X1 >= X1 = ok(U52(X1,X2)) U53(ok(X)) = X >= X = ok(U53(X)) U61(ok(X1),ok(X2)) = X1 >= X1 = ok(U61(X1,X2)) U62(ok(X)) = X >= X = ok(U62(X)) U71(ok(X1),ok(X2)) = X1 >= X1 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isNePal(ok(X)) = 0 >= 0 = ok(isNePal(X)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isPalListKind(ok(X)) = 0 >= 0 = ok(isPalListKind(X)) isPal(ok(X)) = 0 >= 0 = ok(isPal(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt(),V)) -> mark(U12(isNeList(V))) active(U12(tt())) -> mark(tt()) active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2)) active(U22(tt(),V2)) -> mark(U23(isList(V2))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isQid(V))) active(U32(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2)) active(U42(tt(),V2)) -> mark(U43(isNeList(V2))) active(U43(tt())) -> mark(tt()) active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2)) active(U52(tt(),V2)) -> mark(U53(isList(V2))) active(U53(tt())) -> mark(tt()) active(U61(tt(),V)) -> mark(U62(isQid(V))) active(U62(tt())) -> mark(tt()) active(U71(tt(),V)) -> mark(U72(isNePal(V))) active(U72(tt())) -> mark(tt()) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V),V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V),V)) active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V),V)) active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V),V)) active(isPal(nil())) -> mark(tt()) active(isPalListKind(a())) -> mark(tt()) active(isPalListKind(e())) -> mark(tt()) active(isPalListKind(i())) -> mark(tt()) active(isPalListKind(nil())) -> mark(tt()) active(isPalListKind(o())) -> mark(tt()) active(isPalListKind(u())) -> mark(tt()) active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2)) -> U22(active(X1),X2) active(U23(X)) -> U23(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U32(X)) -> U32(active(X)) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2)) -> U42(active(X1),X2) active(U43(X)) -> U43(active(X)) active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) active(U52(X1,X2)) -> U52(active(X1),X2) active(U53(X)) -> U53(active(X)) active(U61(X1,X2)) -> U61(active(X1),X2) active(U62(X)) -> U62(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U62(mark(X)) -> mark(U62(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2)) -> U42(proper(X1),proper(X2)) proper(U43(X)) -> U43(proper(X)) proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U53(X)) -> U53(proper(X)) proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) proper(U62(X)) -> U62(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(isPalListKind(X)) -> isPalListKind(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNeList(ok(X)) -> ok(isNeList(X)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) isList(ok(X)) -> ok(isList(X)) U23(ok(X)) -> ok(U23(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(ok(X)) -> ok(U32(X)) isQid(ok(X)) -> ok(isQid(X)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(ok(X)) -> ok(U43(X)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(ok(X)) -> ok(U53(X)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U62(ok(X)) -> ok(U62(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isNePal(ok(X)) -> ok(isNePal(X)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed