/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES 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)) Usable Rule Processor: 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)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) isNeList(ok(X)) -> ok(isNeList(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) isList(ok(X)) -> ok(isList(X)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) isQid(ok(X)) -> ok(isQid(X)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U43(ok(X)) -> ok(U43(X)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U53(ok(X)) -> ok(U53(X)) U62(mark(X)) -> mark(U62(X)) U62(ok(X)) -> ok(U62(X)) isNePal(ok(X)) -> ok(isNePal(X)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(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()) LPO Processor: argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = [0] pi(nil) = [] pi(tt) = [] pi(U11) = [0,1] pi(isNeList) = [0] pi(U12) = [0] pi(U21) = [0,1,2] pi(isList) = [0] pi(U22) = [0,1] pi(U23) = [0] pi(U31) = [0,1] pi(isQid) = 0 pi(U32) = [0] pi(U41) = [0,1,2] pi(U42) = [0,1] pi(U43) = [0] pi(U51) = [0,1,2] pi(U52) = [0,1] pi(U53) = [0] pi(U61) = [0,1] pi(U62) = [0] pi(U71) = [0,1] pi(isNePal) = [0] pi(U72) = [0] pi(and) = [0,1] pi(isPalListKind) = 0 pi(isPal) = [0] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(proper) = 0 pi(ok) = 0 pi(top#) = 0 usable rules: 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)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) isNeList(ok(X)) -> ok(isNeList(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) isList(ok(X)) -> ok(isList(X)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) isQid(ok(X)) -> ok(isQid(X)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U43(ok(X)) -> ok(U43(X)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U53(ok(X)) -> ok(U53(X)) U62(mark(X)) -> mark(U62(X)) U62(ok(X)) -> ok(U62(X)) isNePal(ok(X)) -> ok(isNePal(X)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(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()) precedence: nil > __ > isPal ~ U41 > U71 > U42 ~ U21 > isNePal ~ U51 ~ U43 ~ U22 > U52 > u ~ isList > U61 ~ U11 > isNeList > U72 ~ U31 > o ~ i ~ e ~ a ~ and ~ U62 ~ U53 ~ U32 ~ U23 ~ U12 > top# ~ ok ~ proper ~ isPalListKind ~ isQid ~ tt ~ mark ~ active problem: DPs: 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)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) isNeList(ok(X)) -> ok(isNeList(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) isList(ok(X)) -> ok(isList(X)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) isQid(ok(X)) -> ok(isQid(X)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U43(ok(X)) -> ok(U43(X)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U53(ok(X)) -> ok(U53(X)) U62(mark(X)) -> mark(U62(X)) U62(ok(X)) -> ok(U62(X)) isNePal(ok(X)) -> ok(isNePal(X)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(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()) Restore Modifier: DPs: 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)) Usable Rule Processor: DPs: 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)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) isNeList(ok(X)) -> ok(isNeList(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) isList(ok(X)) -> ok(isList(X)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) isQid(ok(X)) -> ok(isQid(X)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U43(ok(X)) -> ok(U43(X)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U53(ok(X)) -> ok(U53(X)) U62(mark(X)) -> mark(U62(X)) U62(ok(X)) -> ok(U62(X)) isNePal(ok(X)) -> ok(isNePal(X)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) KBO Processor: argument filtering: pi(__) = [1] pi(active) = 0 pi(mark) = [] pi(nil) = [] pi(tt) = [] pi(U11) = [0,1] pi(isNeList) = [] pi(U12) = 0 pi(U21) = [1,2] pi(isList) = [] pi(U22) = 0 pi(U23) = 0 pi(U31) = 0 pi(isQid) = [] pi(U32) = 0 pi(U41) = [2] pi(U42) = [1] pi(U43) = 0 pi(U51) = 0 pi(U52) = 0 pi(U53) = 0 pi(U61) = 0 pi(U62) = 0 pi(U71) = [1] pi(isNePal) = [] pi(U72) = 0 pi(and) = 0 pi(isPalListKind) = [] pi(isPal) = [] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(ok) = [0] pi(top#) = 0 usable rules: 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)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U43(ok(X)) -> ok(U43(X)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U53(ok(X)) -> ok(U53(X)) U62(mark(X)) -> mark(U62(X)) U62(ok(X)) -> ok(U62(X)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) weight function: w0 = 1 w(top#) = w(ok) = w(u) = w(o) = w(i) = w(e) = w(a) = w(isPal) = w( isPalListKind) = w(and) = w(isNePal) = w(U71) = w(U42) = w( U41) = w(isQid) = w(U31) = w(isList) = w(isNeList) = w(tt) = w( nil) = w(mark) = w(__) = 1 w(U72) = w(U62) = w(U61) = w(U53) = w(U52) = w(U51) = w(U43) = w( U32) = w(U23) = w(U22) = w(U21) = w(U12) = w(U11) = w(active) = 0 precedence: U42 ~ U41 > tt > isPal ~ isPalListKind ~ isNePal ~ U71 ~ isQid ~ isList ~ isNeList ~ __ > top# ~ ok ~ u ~ o ~ i ~ e ~ a ~ and ~ U72 ~ U62 ~ U61 ~ U53 ~ U52 ~ U51 ~ U43 ~ U32 ~ U31 ~ U23 ~ U22 ~ U21 ~ U12 ~ U11 ~ nil ~ mark ~ active 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)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) isNeList(ok(X)) -> ok(isNeList(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) isList(ok(X)) -> ok(isList(X)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) isQid(ok(X)) -> ok(isQid(X)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U42(mark(X1),X2) -> mark(U42(X1,X2)) U42(ok(X1),ok(X2)) -> ok(U42(X1,X2)) U43(mark(X)) -> mark(U43(X)) U43(ok(X)) -> ok(U43(X)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U53(mark(X)) -> mark(U53(X)) U53(ok(X)) -> ok(U53(X)) U62(mark(X)) -> mark(U62(X)) U62(ok(X)) -> ok(U62(X)) isNePal(ok(X)) -> ok(isNePal(X)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) isPalListKind(ok(X)) -> ok(isPalListKind(X)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) U61(mark(X1),X2) -> mark(U61(X1,X2)) U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) isPal(ok(X)) -> ok(isPal(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) Qed 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)) Subterm Criterion Processor: simple projection: pi(active#) = 0 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)) Subterm Criterion Processor: simple projection: pi(proper#) = 0 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)) Subterm Criterion Processor: simple projection: pi(isPal#) = 0 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)) Subterm Criterion Processor: simple projection: pi(isPalListKind#) = 0 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)) Subterm Criterion Processor: simple projection: pi(and#) = 0 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)) Subterm Criterion Processor: simple projection: pi(isNePal#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U72#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U71#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U62#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U61#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U53#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U52#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U51#) = 1 problem: DPs: U51#(mark(X1),X2,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)) Subterm Criterion Processor: simple projection: pi(U51#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U43#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U42#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U41#) = 1 problem: DPs: U41#(mark(X1),X2,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)) Subterm Criterion Processor: simple projection: pi(U41#) = 0 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)) Subterm Criterion Processor: simple projection: pi(isQid#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U32#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U31#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U23#) = 0 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)) Subterm Criterion Processor: simple projection: pi(isList#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U22#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U21#) = 1 problem: DPs: U21#(mark(X1),X2,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)) Subterm Criterion Processor: simple projection: pi(U21#) = 0 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)) Subterm Criterion Processor: simple projection: pi(isNeList#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U12#) = 0 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)) Subterm Criterion Processor: simple projection: pi(U11#) = 0 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)) Subterm Criterion Processor: simple projection: pi(__#) = 0 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)) Subterm Criterion Processor: simple projection: pi(__#) = 1 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