/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR I P V V1 V2 X X1 X2 Y Z) (RULES U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ) Problem 1: Dependency Pairs Processor: -> Pairs: U11#(mark(X)) -> U11#(X) U11#(ok(X)) -> U11#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(ok(X1),ok(X2)) -> U21#(X1,X2) U22#(mark(X)) -> U22#(X) U22#(ok(X)) -> U22#(X) U31#(mark(X)) -> U31#(X) U31#(ok(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(ok(X1),ok(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(ok(X)) -> U42#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(ok(X1),ok(X2)) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(ok(X)) -> U52#(X) U61#(mark(X)) -> U61#(X) U61#(ok(X)) -> U61#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) U72#(ok(X)) -> U72#(X) U81#(mark(X)) -> U81#(X) U81#(ok(X)) -> U81#(X) __#(mark(X1),X2) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) ACTIVE(U11(X)) -> U11#(active(X)) ACTIVE(U11(X)) -> ACTIVE(X) ACTIVE(U21(tt,V2)) -> U22#(isList(V2)) ACTIVE(U21(tt,V2)) -> ISLIST(V2) ACTIVE(U21(X1,X2)) -> U21#(active(X1),X2) ACTIVE(U21(X1,X2)) -> ACTIVE(X1) ACTIVE(U22(X)) -> U22#(active(X)) ACTIVE(U22(X)) -> ACTIVE(X) ACTIVE(U31(X)) -> U31#(active(X)) ACTIVE(U31(X)) -> ACTIVE(X) ACTIVE(U41(tt,V2)) -> U42#(isNeList(V2)) ACTIVE(U41(tt,V2)) -> ISNELIST(V2) ACTIVE(U41(X1,X2)) -> U41#(active(X1),X2) ACTIVE(U41(X1,X2)) -> ACTIVE(X1) ACTIVE(U42(X)) -> U42#(active(X)) ACTIVE(U42(X)) -> ACTIVE(X) ACTIVE(U51(tt,V2)) -> U52#(isList(V2)) ACTIVE(U51(tt,V2)) -> ISLIST(V2) ACTIVE(U51(X1,X2)) -> U51#(active(X1),X2) ACTIVE(U51(X1,X2)) -> ACTIVE(X1) ACTIVE(U52(X)) -> U52#(active(X)) ACTIVE(U52(X)) -> ACTIVE(X) ACTIVE(U61(X)) -> U61#(active(X)) ACTIVE(U61(X)) -> ACTIVE(X) ACTIVE(U71(tt,P)) -> U72#(isPal(P)) ACTIVE(U71(tt,P)) -> ISPAL(P) ACTIVE(U71(X1,X2)) -> U71#(active(X1),X2) ACTIVE(U71(X1,X2)) -> ACTIVE(X1) ACTIVE(U72(X)) -> U72#(active(X)) ACTIVE(U72(X)) -> ACTIVE(X) ACTIVE(U81(X)) -> U81#(active(X)) ACTIVE(U81(X)) -> ACTIVE(X) ACTIVE(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) ACTIVE(__(__(X,Y),Z)) -> __#(Y,Z) ACTIVE(__(X1,X2)) -> __#(active(X1),X2) ACTIVE(__(X1,X2)) -> __#(X1,active(X2)) ACTIVE(__(X1,X2)) -> ACTIVE(X1) ACTIVE(__(X1,X2)) -> ACTIVE(X2) ACTIVE(isList(__(V1,V2))) -> U21#(isList(V1),V2) ACTIVE(isList(__(V1,V2))) -> ISLIST(V1) ACTIVE(isList(V)) -> U11#(isNeList(V)) ACTIVE(isList(V)) -> ISNELIST(V) ACTIVE(isNeList(__(V1,V2))) -> U41#(isList(V1),V2) ACTIVE(isNeList(__(V1,V2))) -> U51#(isNeList(V1),V2) ACTIVE(isNeList(__(V1,V2))) -> ISLIST(V1) ACTIVE(isNeList(__(V1,V2))) -> ISNELIST(V1) ACTIVE(isNeList(V)) -> U31#(isQid(V)) ACTIVE(isNeList(V)) -> ISQID(V) ACTIVE(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),P) ACTIVE(isNePal(__(I,__(P,I)))) -> ISQID(I) ACTIVE(isNePal(V)) -> U61#(isQid(V)) ACTIVE(isNePal(V)) -> ISQID(V) ACTIVE(isPal(V)) -> U81#(isNePal(V)) ACTIVE(isPal(V)) -> ISNEPAL(V) ISLIST(ok(X)) -> ISLIST(X) ISNELIST(ok(X)) -> ISNELIST(X) ISNEPAL(ok(X)) -> ISNEPAL(X) ISPAL(ok(X)) -> ISPAL(X) ISQID(ok(X)) -> ISQID(X) PROPER(U11(X)) -> U11#(proper(X)) PROPER(U11(X)) -> PROPER(X) PROPER(U21(X1,X2)) -> U21#(proper(X1),proper(X2)) PROPER(U21(X1,X2)) -> PROPER(X1) PROPER(U21(X1,X2)) -> PROPER(X2) PROPER(U22(X)) -> U22#(proper(X)) PROPER(U22(X)) -> PROPER(X) PROPER(U31(X)) -> U31#(proper(X)) PROPER(U31(X)) -> PROPER(X) PROPER(U41(X1,X2)) -> U41#(proper(X1),proper(X2)) PROPER(U41(X1,X2)) -> PROPER(X1) PROPER(U41(X1,X2)) -> PROPER(X2) PROPER(U42(X)) -> U42#(proper(X)) PROPER(U42(X)) -> PROPER(X) PROPER(U51(X1,X2)) -> U51#(proper(X1),proper(X2)) PROPER(U51(X1,X2)) -> PROPER(X1) PROPER(U51(X1,X2)) -> PROPER(X2) PROPER(U52(X)) -> U52#(proper(X)) PROPER(U52(X)) -> PROPER(X) PROPER(U61(X)) -> U61#(proper(X)) PROPER(U61(X)) -> PROPER(X) PROPER(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) PROPER(U71(X1,X2)) -> PROPER(X1) PROPER(U71(X1,X2)) -> PROPER(X2) PROPER(U72(X)) -> U72#(proper(X)) PROPER(U72(X)) -> PROPER(X) PROPER(U81(X)) -> U81#(proper(X)) PROPER(U81(X)) -> PROPER(X) PROPER(__(X1,X2)) -> __#(proper(X1),proper(X2)) PROPER(__(X1,X2)) -> PROPER(X1) PROPER(__(X1,X2)) -> PROPER(X2) PROPER(isList(X)) -> ISLIST(proper(X)) PROPER(isList(X)) -> PROPER(X) PROPER(isNeList(X)) -> ISNELIST(proper(X)) PROPER(isNeList(X)) -> PROPER(X) PROPER(isNePal(X)) -> ISNEPAL(proper(X)) PROPER(isNePal(X)) -> PROPER(X) PROPER(isPal(X)) -> ISPAL(proper(X)) PROPER(isPal(X)) -> PROPER(X) PROPER(isQid(X)) -> ISQID(proper(X)) PROPER(isQid(X)) -> PROPER(X) TOP(mark(X)) -> PROPER(X) TOP(mark(X)) -> TOP(proper(X)) TOP(ok(X)) -> ACTIVE(X) TOP(ok(X)) -> TOP(active(X)) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Problem 1: SCC Processor: -> Pairs: U11#(mark(X)) -> U11#(X) U11#(ok(X)) -> U11#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(ok(X1),ok(X2)) -> U21#(X1,X2) U22#(mark(X)) -> U22#(X) U22#(ok(X)) -> U22#(X) U31#(mark(X)) -> U31#(X) U31#(ok(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(ok(X1),ok(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(ok(X)) -> U42#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(ok(X1),ok(X2)) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(ok(X)) -> U52#(X) U61#(mark(X)) -> U61#(X) U61#(ok(X)) -> U61#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) U72#(ok(X)) -> U72#(X) U81#(mark(X)) -> U81#(X) U81#(ok(X)) -> U81#(X) __#(mark(X1),X2) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) ACTIVE(U11(X)) -> U11#(active(X)) ACTIVE(U11(X)) -> ACTIVE(X) ACTIVE(U21(tt,V2)) -> U22#(isList(V2)) ACTIVE(U21(tt,V2)) -> ISLIST(V2) ACTIVE(U21(X1,X2)) -> U21#(active(X1),X2) ACTIVE(U21(X1,X2)) -> ACTIVE(X1) ACTIVE(U22(X)) -> U22#(active(X)) ACTIVE(U22(X)) -> ACTIVE(X) ACTIVE(U31(X)) -> U31#(active(X)) ACTIVE(U31(X)) -> ACTIVE(X) ACTIVE(U41(tt,V2)) -> U42#(isNeList(V2)) ACTIVE(U41(tt,V2)) -> ISNELIST(V2) ACTIVE(U41(X1,X2)) -> U41#(active(X1),X2) ACTIVE(U41(X1,X2)) -> ACTIVE(X1) ACTIVE(U42(X)) -> U42#(active(X)) ACTIVE(U42(X)) -> ACTIVE(X) ACTIVE(U51(tt,V2)) -> U52#(isList(V2)) ACTIVE(U51(tt,V2)) -> ISLIST(V2) ACTIVE(U51(X1,X2)) -> U51#(active(X1),X2) ACTIVE(U51(X1,X2)) -> ACTIVE(X1) ACTIVE(U52(X)) -> U52#(active(X)) ACTIVE(U52(X)) -> ACTIVE(X) ACTIVE(U61(X)) -> U61#(active(X)) ACTIVE(U61(X)) -> ACTIVE(X) ACTIVE(U71(tt,P)) -> U72#(isPal(P)) ACTIVE(U71(tt,P)) -> ISPAL(P) ACTIVE(U71(X1,X2)) -> U71#(active(X1),X2) ACTIVE(U71(X1,X2)) -> ACTIVE(X1) ACTIVE(U72(X)) -> U72#(active(X)) ACTIVE(U72(X)) -> ACTIVE(X) ACTIVE(U81(X)) -> U81#(active(X)) ACTIVE(U81(X)) -> ACTIVE(X) ACTIVE(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) ACTIVE(__(__(X,Y),Z)) -> __#(Y,Z) ACTIVE(__(X1,X2)) -> __#(active(X1),X2) ACTIVE(__(X1,X2)) -> __#(X1,active(X2)) ACTIVE(__(X1,X2)) -> ACTIVE(X1) ACTIVE(__(X1,X2)) -> ACTIVE(X2) ACTIVE(isList(__(V1,V2))) -> U21#(isList(V1),V2) ACTIVE(isList(__(V1,V2))) -> ISLIST(V1) ACTIVE(isList(V)) -> U11#(isNeList(V)) ACTIVE(isList(V)) -> ISNELIST(V) ACTIVE(isNeList(__(V1,V2))) -> U41#(isList(V1),V2) ACTIVE(isNeList(__(V1,V2))) -> U51#(isNeList(V1),V2) ACTIVE(isNeList(__(V1,V2))) -> ISLIST(V1) ACTIVE(isNeList(__(V1,V2))) -> ISNELIST(V1) ACTIVE(isNeList(V)) -> U31#(isQid(V)) ACTIVE(isNeList(V)) -> ISQID(V) ACTIVE(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),P) ACTIVE(isNePal(__(I,__(P,I)))) -> ISQID(I) ACTIVE(isNePal(V)) -> U61#(isQid(V)) ACTIVE(isNePal(V)) -> ISQID(V) ACTIVE(isPal(V)) -> U81#(isNePal(V)) ACTIVE(isPal(V)) -> ISNEPAL(V) ISLIST(ok(X)) -> ISLIST(X) ISNELIST(ok(X)) -> ISNELIST(X) ISNEPAL(ok(X)) -> ISNEPAL(X) ISPAL(ok(X)) -> ISPAL(X) ISQID(ok(X)) -> ISQID(X) PROPER(U11(X)) -> U11#(proper(X)) PROPER(U11(X)) -> PROPER(X) PROPER(U21(X1,X2)) -> U21#(proper(X1),proper(X2)) PROPER(U21(X1,X2)) -> PROPER(X1) PROPER(U21(X1,X2)) -> PROPER(X2) PROPER(U22(X)) -> U22#(proper(X)) PROPER(U22(X)) -> PROPER(X) PROPER(U31(X)) -> U31#(proper(X)) PROPER(U31(X)) -> PROPER(X) PROPER(U41(X1,X2)) -> U41#(proper(X1),proper(X2)) PROPER(U41(X1,X2)) -> PROPER(X1) PROPER(U41(X1,X2)) -> PROPER(X2) PROPER(U42(X)) -> U42#(proper(X)) PROPER(U42(X)) -> PROPER(X) PROPER(U51(X1,X2)) -> U51#(proper(X1),proper(X2)) PROPER(U51(X1,X2)) -> PROPER(X1) PROPER(U51(X1,X2)) -> PROPER(X2) PROPER(U52(X)) -> U52#(proper(X)) PROPER(U52(X)) -> PROPER(X) PROPER(U61(X)) -> U61#(proper(X)) PROPER(U61(X)) -> PROPER(X) PROPER(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) PROPER(U71(X1,X2)) -> PROPER(X1) PROPER(U71(X1,X2)) -> PROPER(X2) PROPER(U72(X)) -> U72#(proper(X)) PROPER(U72(X)) -> PROPER(X) PROPER(U81(X)) -> U81#(proper(X)) PROPER(U81(X)) -> PROPER(X) PROPER(__(X1,X2)) -> __#(proper(X1),proper(X2)) PROPER(__(X1,X2)) -> PROPER(X1) PROPER(__(X1,X2)) -> PROPER(X2) PROPER(isList(X)) -> ISLIST(proper(X)) PROPER(isList(X)) -> PROPER(X) PROPER(isNeList(X)) -> ISNELIST(proper(X)) PROPER(isNeList(X)) -> PROPER(X) PROPER(isNePal(X)) -> ISNEPAL(proper(X)) PROPER(isNePal(X)) -> PROPER(X) PROPER(isPal(X)) -> ISPAL(proper(X)) PROPER(isPal(X)) -> PROPER(X) PROPER(isQid(X)) -> ISQID(proper(X)) PROPER(isQid(X)) -> PROPER(X) TOP(mark(X)) -> PROPER(X) TOP(mark(X)) -> TOP(proper(X)) TOP(ok(X)) -> ACTIVE(X) TOP(ok(X)) -> TOP(active(X)) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ISQID(ok(X)) -> ISQID(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: ISPAL(ok(X)) -> ISPAL(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: ISNEPAL(ok(X)) -> ISNEPAL(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: ISNELIST(ok(X)) -> ISNELIST(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: ISLIST(ok(X)) -> ISLIST(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: __#(mark(X1),X2) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U81#(mark(X)) -> U81#(X) U81#(ok(X)) -> U81#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U72#(mark(X)) -> U72#(X) U72#(ok(X)) -> U72#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U71#(mark(X1),X2) -> U71#(X1,X2) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U61#(mark(X)) -> U61#(X) U61#(ok(X)) -> U61#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U52#(mark(X)) -> U52#(X) U52#(ok(X)) -> U52#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(ok(X1),ok(X2)) -> U51#(X1,X2) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U42#(mark(X)) -> U42#(X) U42#(ok(X)) -> U42#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U41#(mark(X1),X2) -> U41#(X1,X2) U41#(ok(X1),ok(X2)) -> U41#(X1,X2) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U31#(mark(X)) -> U31#(X) U31#(ok(X)) -> U31#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U22#(mark(X)) -> U22#(X) U22#(ok(X)) -> U22#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U21#(mark(X1),X2) -> U21#(X1,X2) U21#(ok(X1),ok(X2)) -> U21#(X1,X2) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: U11#(mark(X)) -> U11#(X) U11#(ok(X)) -> U11#(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: ACTIVE(U11(X)) -> ACTIVE(X) ACTIVE(U21(X1,X2)) -> ACTIVE(X1) ACTIVE(U22(X)) -> ACTIVE(X) ACTIVE(U31(X)) -> ACTIVE(X) ACTIVE(U41(X1,X2)) -> ACTIVE(X1) ACTIVE(U42(X)) -> ACTIVE(X) ACTIVE(U51(X1,X2)) -> ACTIVE(X1) ACTIVE(U52(X)) -> ACTIVE(X) ACTIVE(U61(X)) -> ACTIVE(X) ACTIVE(U71(X1,X2)) -> ACTIVE(X1) ACTIVE(U72(X)) -> ACTIVE(X) ACTIVE(U81(X)) -> ACTIVE(X) ACTIVE(__(X1,X2)) -> ACTIVE(X1) ACTIVE(__(X1,X2)) -> ACTIVE(X2) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: PROPER(U11(X)) -> PROPER(X) PROPER(U21(X1,X2)) -> PROPER(X1) PROPER(U21(X1,X2)) -> PROPER(X2) PROPER(U22(X)) -> PROPER(X) PROPER(U31(X)) -> PROPER(X) PROPER(U41(X1,X2)) -> PROPER(X1) PROPER(U41(X1,X2)) -> PROPER(X2) PROPER(U42(X)) -> PROPER(X) PROPER(U51(X1,X2)) -> PROPER(X1) PROPER(U51(X1,X2)) -> PROPER(X2) PROPER(U52(X)) -> PROPER(X) PROPER(U61(X)) -> PROPER(X) PROPER(U71(X1,X2)) -> PROPER(X1) PROPER(U71(X1,X2)) -> PROPER(X2) PROPER(U72(X)) -> PROPER(X) PROPER(U81(X)) -> PROPER(X) PROPER(__(X1,X2)) -> PROPER(X1) PROPER(__(X1,X2)) -> PROPER(X2) PROPER(isList(X)) -> PROPER(X) PROPER(isNeList(X)) -> PROPER(X) PROPER(isNePal(X)) -> PROPER(X) PROPER(isPal(X)) -> PROPER(X) PROPER(isQid(X)) -> PROPER(X) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->->Cycle: ->->-> Pairs: TOP(mark(X)) -> TOP(proper(X)) TOP(ok(X)) -> TOP(active(X)) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) The problem is decomposed in 21 subproblems. Problem 1.1: Subterm Processor: -> Pairs: ISQID(ok(X)) -> ISQID(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(ISQID) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: ISPAL(ok(X)) -> ISPAL(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(ISPAL) = 1 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Subterm Processor: -> Pairs: ISNEPAL(ok(X)) -> ISNEPAL(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(ISNEPAL) = 1 Problem 1.3: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.4: Subterm Processor: -> Pairs: ISNELIST(ok(X)) -> ISNELIST(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(ISNELIST) = 1 Problem 1.4: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.5: Subterm Processor: -> Pairs: ISLIST(ok(X)) -> ISLIST(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(ISLIST) = 1 Problem 1.5: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.6: Subterm Processor: -> Pairs: __#(mark(X1),X2) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(__#) = 1 Problem 1.6: SCC Processor: -> Pairs: __#(X1,mark(X2)) -> __#(X1,X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: __#(X1,mark(X2)) -> __#(X1,X2) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Problem 1.6: Subterm Processor: -> Pairs: __#(X1,mark(X2)) -> __#(X1,X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(__#) = 2 Problem 1.6: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.7: Subterm Processor: -> Pairs: U81#(mark(X)) -> U81#(X) U81#(ok(X)) -> U81#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U81#) = 1 Problem 1.7: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.8: Subterm Processor: -> Pairs: U72#(mark(X)) -> U72#(X) U72#(ok(X)) -> U72#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U72#) = 1 Problem 1.8: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.9: Subterm Processor: -> Pairs: U71#(mark(X1),X2) -> U71#(X1,X2) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U71#) = 1 Problem 1.9: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.10: Subterm Processor: -> Pairs: U61#(mark(X)) -> U61#(X) U61#(ok(X)) -> U61#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U61#) = 1 Problem 1.10: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.11: Subterm Processor: -> Pairs: U52#(mark(X)) -> U52#(X) U52#(ok(X)) -> U52#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U52#) = 1 Problem 1.11: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.12: Subterm Processor: -> Pairs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(ok(X1),ok(X2)) -> U51#(X1,X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U51#) = 1 Problem 1.12: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.13: Subterm Processor: -> Pairs: U42#(mark(X)) -> U42#(X) U42#(ok(X)) -> U42#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U42#) = 1 Problem 1.13: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.14: Subterm Processor: -> Pairs: U41#(mark(X1),X2) -> U41#(X1,X2) U41#(ok(X1),ok(X2)) -> U41#(X1,X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U41#) = 1 Problem 1.14: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.15: Subterm Processor: -> Pairs: U31#(mark(X)) -> U31#(X) U31#(ok(X)) -> U31#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U31#) = 1 Problem 1.15: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.16: Subterm Processor: -> Pairs: U22#(mark(X)) -> U22#(X) U22#(ok(X)) -> U22#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U22#) = 1 Problem 1.16: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.17: Subterm Processor: -> Pairs: U21#(mark(X1),X2) -> U21#(X1,X2) U21#(ok(X1),ok(X2)) -> U21#(X1,X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U21#) = 1 Problem 1.17: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.18: Subterm Processor: -> Pairs: U11#(mark(X)) -> U11#(X) U11#(ok(X)) -> U11#(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(U11#) = 1 Problem 1.18: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.19: Subterm Processor: -> Pairs: ACTIVE(U11(X)) -> ACTIVE(X) ACTIVE(U21(X1,X2)) -> ACTIVE(X1) ACTIVE(U22(X)) -> ACTIVE(X) ACTIVE(U31(X)) -> ACTIVE(X) ACTIVE(U41(X1,X2)) -> ACTIVE(X1) ACTIVE(U42(X)) -> ACTIVE(X) ACTIVE(U51(X1,X2)) -> ACTIVE(X1) ACTIVE(U52(X)) -> ACTIVE(X) ACTIVE(U61(X)) -> ACTIVE(X) ACTIVE(U71(X1,X2)) -> ACTIVE(X1) ACTIVE(U72(X)) -> ACTIVE(X) ACTIVE(U81(X)) -> ACTIVE(X) ACTIVE(__(X1,X2)) -> ACTIVE(X1) ACTIVE(__(X1,X2)) -> ACTIVE(X2) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(ACTIVE) = 1 Problem 1.19: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.20: Subterm Processor: -> Pairs: PROPER(U11(X)) -> PROPER(X) PROPER(U21(X1,X2)) -> PROPER(X1) PROPER(U21(X1,X2)) -> PROPER(X2) PROPER(U22(X)) -> PROPER(X) PROPER(U31(X)) -> PROPER(X) PROPER(U41(X1,X2)) -> PROPER(X1) PROPER(U41(X1,X2)) -> PROPER(X2) PROPER(U42(X)) -> PROPER(X) PROPER(U51(X1,X2)) -> PROPER(X1) PROPER(U51(X1,X2)) -> PROPER(X2) PROPER(U52(X)) -> PROPER(X) PROPER(U61(X)) -> PROPER(X) PROPER(U71(X1,X2)) -> PROPER(X1) PROPER(U71(X1,X2)) -> PROPER(X2) PROPER(U72(X)) -> PROPER(X) PROPER(U81(X)) -> PROPER(X) PROPER(__(X1,X2)) -> PROPER(X1) PROPER(__(X1,X2)) -> PROPER(X2) PROPER(isList(X)) -> PROPER(X) PROPER(isNeList(X)) -> PROPER(X) PROPER(isNePal(X)) -> PROPER(X) PROPER(isPal(X)) -> PROPER(X) PROPER(isQid(X)) -> PROPER(X) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Projection: pi(PROPER) = 1 Problem 1.20: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.21: Reduction Pair Processor: -> Pairs: TOP(mark(X)) -> TOP(proper(X)) TOP(ok(X)) -> TOP(active(X)) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) -> Usable rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X) = X + 1/2 [U21](X1,X2) = X1 + 2.X2 + 1 [U22](X) = X + 1/2 [U31](X) = X + 1/2 [U41](X1,X2) = X1 + 2.X2 [U42](X) = X + 1/2 [U51](X1,X2) = 2.X1 + 2.X2 [U52](X) = X + 1 [U61](X) = X + 1/2 [U71](X1,X2) = 2.X1 + 2.X2 [U72](X) = X + 1/2 [U81](X) = X + 1/2 [__](X1,X2) = 2.X1 + X2 + 1 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 1 [isNePal](X) = 2.X + 1 [isPal](X) = 2.X + 2 [isQid](X) = 2.X [proper](X) = X [a] = 2 [e] = 2 [i] = 2 [mark](X) = X + 1/2 [nil] = 2 [o] = 2 [ok](X) = X [tt] = 2 [u] = 2 [TOP](X) = 2.X Problem 1.21: SCC Processor: -> Pairs: TOP(ok(X)) -> TOP(active(X)) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: TOP(ok(X)) -> TOP(active(X)) ->->-> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Problem 1.21: Reduction Pair Processor: -> Pairs: TOP(ok(X)) -> TOP(active(X)) -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) -> Usable rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [U11](X) = 2.X + 1 [U21](X1,X2) = 2.X2 + 2 [U22](X) = X [U31](X) = 2.X + 2 [U41](X1,X2) = 2.X1 + 1 [U42](X) = X [U51](X1,X2) = 2.X1 + 1 [U52](X) = 2.X + 2 [U61](X) = 2.X + 2 [U71](X1,X2) = X1 + 2.X2 + 2 [U72](X) = 2.X + 2 [U81](X) = 2.X + 1 [__](X1,X2) = 2.X1 + X2 + 2 [active](X) = X [isList](X) = 2.X + 2 [isNeList](X) = 2.X + 2 [isNePal](X) = 2.X + 2 [isPal](X) = 2.X + 2 [isQid](X) = 2.X + 2 [a] = 0 [e] = 2 [i] = 2 [mark](X) = 2 [nil] = 2 [o] = 2 [ok](X) = 2.X + 2 [tt] = 2 [u] = 2 [TOP](X) = X Problem 1.21: SCC Processor: -> Pairs: Empty -> Rules: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) active(U11(tt)) -> mark(tt) active(U11(X)) -> U11(active(X)) active(U21(tt,V2)) -> mark(U22(isList(V2))) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(tt)) -> mark(tt) active(U22(X)) -> U22(active(X)) active(U31(tt)) -> mark(tt) active(U31(X)) -> U31(active(X)) active(U41(tt,V2)) -> mark(U42(isNeList(V2))) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(tt)) -> mark(tt) active(U42(X)) -> U42(active(X)) active(U51(tt,V2)) -> mark(U52(isList(V2))) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(tt)) -> mark(tt) active(U52(X)) -> U52(active(X)) active(U61(tt)) -> mark(tt) active(U61(X)) -> U61(active(X)) active(U71(tt,P)) -> mark(U72(isPal(P))) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(tt)) -> mark(tt) active(U72(X)) -> U72(active(X)) active(U81(tt)) -> mark(tt) active(U81(X)) -> U81(active(X)) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil,X)) -> mark(X) active(__(X,nil)) -> mark(X) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil)) -> mark(tt) active(isList(V)) -> mark(U11(isNeList(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(nil)) -> mark(tt) active(isPal(V)) -> mark(U81(isNePal(V))) 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) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(a) -> ok(a) proper(e) -> ok(e) proper(i) -> ok(i) proper(nil) -> ok(nil) proper(o) -> ok(o) proper(tt) -> ok(tt) proper(u) -> ok(u) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) ->Strongly Connected Components: There is no strongly connected component The problem is finite.